Published by 9 December 1925, Göttingen (1925)

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**Item Description: **9 December 1925, Göttingen, 1925. Historically important, very detailed, scientific letter showing how Heisenberg, who had invented quantum mechanics just six months earlier, grappled with the difficulties presented by a basic new discovery in quantum physics, that of electron spin by Goudsmit and George Uhlenbeck. When this letter was written, Heisenberg was not convinced that their proposal was correct, citing in this letter calculations he has carried out (partly with Pascual Jordan) which show that Goudsmit and Uhlenbeck’s theory predicts a splitting of spectral lines twice as large as the observed values. Nevertheless, Heisenberg was keeping an open mind, and following a meeting with Niels Bohr in Göttingen just a few days after this letter, he accepted the concept of electron spin, even though the paradoxical factor of two remained unresolved. Later in the letter Heisenberg is, even at this early stage in the development of quantum mechanics, starting to think about the quantum theory of radiation, later called quantum electrodynamics. Heisenberg was at this time teaching at the University of Göttingen, having studied there under Arnold Sommerfeld and Max Born.Translated, the letter reads, in full: Many thanks for the two letters. Forgive me that I didn't answer you earlier. In the meantime I have often thought about your theory and I am convinced that you have brought to light a new and important facet of the phenomenon of multiplet structures. Of course I also believe that the ultimate result lies even deeper and that it is really related to a multi-dimensional invariant formulation of quantum mechanics. I think that there are some arguments against the literal use of your hypothesis. First of all, there is this factor 2 which really prevents a direct agreement with experiment. Then you must also think of the triplet spectra. The distance between a singlet and a triplet system for a given value of C would have to result from the different orientations of the electrons’ spins relative to each other. Classically, the energy of such an interaction would be much smaller than the distance between singlet and triplet. But it seems to me that in this case one does get the correct order of magnitude. In spite of all this I can clearly see the progress contained in your hypothesis. I suspect that the agreement between your formula and the relativistic formula cannot be an accident. At the moment I am researching here with Jordan a four-dimensional formulation of quantum mechanics and I am curious to find out what becomes of it. It is obvious that, so far, quantum mechanics has stood in conflict with the relativity theory; for instance, an empty cavity, viewed as an oscillator, would have to have non-zero energy, but in spite of that one would not like to attribute a positive mass to it. I really don't know how one can put the muliplets in order. The Copenhagen people [i.e. Bohr's laboratory staff] should have sent you some excerpts of my work, but they are so awfully slow there. When the visible lines of the spectrum of hydrogen are observed in a powerful spectroscope, they appear as close doublets. In atoms having two electrons outside the closed core, or shell, of electrons the lines are split into triplets. Higher multiplets are also possible. This phenomenon, known as fine structure, was established experimentally around 1890 but did not receive an explanation until Sommerfeld’s theory of 1915-16, which had wide influence through its detailed treatment in Sommerfeld’s classic textbook Atombau und Spektrallinien (1919). Sommerfeld modified Bohr’s treatment of the hydrogen atom from 1913 by taking into account the theory of relativity, in particular the variation in the mass of the revolving electron – hence Heisenberg refers to the ‘relativistic formula’ in his letter. Sommerfeld’s theory was accepted by most physicists until near the end of the reign of the ‘old’ quantum theory in 1925, but by that time a number of discrepancies had been found between exper. Bookseller Inventory # 3869

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Published by 1929-1930 (1929)

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**Item Description: **1929-1930, 1929. Heisenberg, Werner (1901-76) and Wolfgang Pauli (1900-1958). (1) Zur Quantendynamik der Wellenfelder. Offprint from Zeitschrift für Physik 56 (1929). 61pp. 231 x 160 mm. Original printed wrappers, spine repaired. (2) Zur Quantentheorie der Wellenfelder. II. Offprint from Zeitschrift für Physik 59 (1930). 168-190pp. 231 x 160 mm. Original printed wrappers, spine repaired with clear tape. Together 2 items. Small mark from paper clip on wrappers of no. (1), small tear in front wrapper of no. (2), but very good. First Editions, Offprint Issues. Heisenberg and Pauli’s two-part paper contains the first full-fledged relativistic quantum field theory, representing the "formal invention of quantum electrodynamics" (Miller, Early Quantum Electrodynamics: A Source Book, p. xiii). "This extremely technical and mathematical branch of quantum physics, the foundations of which were laid by Heisenberg, Dirac, Pauli, Jordan, and their colleagues during the late 1920s and early 1930s, continues to this day with much the same program and approach . . . [Heisenberg was] a leading member of the small band of abstract theorists who established the program and laid the foundations of relativistic quantum field theory as it has been pursued ever since" (Cassidy, Uncertainty: The Life and Science of Werner Heisenberg, p. 276). In this paper—the only one that Heisenberg and Pauli co-authored—the two physicists attempted to establish "a consistent extension of the quantum formalism that would yield a satisfactory unification of quantum mechanics and relativity theory . . . In 1929, drawing upon the work of Dirac, Jordan, Oskar Klein, and others, Heisenberg and Pauli succeeded in formulating a general gauge-invariant relativistic quantum field theory by treating particles and fields as separate entities interacting through the intermediaries of field quanta. The formalism led to the creation of a relativistic quantum electrodynamics, equivalent to that developed by Dirac, which, despite its puzzling negative energy states, seemed satisfactory at low energies and small orders of interaction. But at high energies, where particles approach closer than their radii, the interaction energy diverges to infinity. Even at rest, a lone electron interacting with its own field seemed to possess an infinite self-energy . . . Attention was directed to the resolution of such difficulties for more than two decades" (Dictionary of Scientific Biography). Mehra & Rechenberg, The Historical Development of Quantum Theory, 6, pp. 312-26. Bookseller Inventory # 43254

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Published by Julius Springer, Berlin (1925)

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From: Manhattan Rare Book Company, ABAA, ILAB (New York, NY, U.S.A.)

**Item Description: **Julius Springer, Berlin, 1925. Hardcover. Book Condition: Very Good. 1st Edition. FIRST EDITIONS of three papers that defined a discipline: THE THEORETICAL FOUNDATION FOR QUANTUM MECHANICS. "In May 1925, Heisenberg deliberately abandoned the classical picture of particles and orbits, and took a long, hard look at the mathematics that describes the associations between pairs of quantum states, without asking himself how the quantum entity gets from state A to state B. In the summer of 1925, working with Pasqual Jordan, Born translated Heisenberg's mathematical insight into the formal language of matrices, and Born, Heisenberg and Jordan together published a full account of the work, in what became known as the 'three-man paper'. The equations of Newtonian (classical) mechanics were replaced by similar equations involving matrices, and many of the fundamental concepts of classical mechanics- such as the conservation of energy- emerged naturally from the new equations. Matrix mechanics seemed to contain Newtonian Mechanics within itself, in much the same way that the equations of the general theory of relativity include the Newtonian description of gravity as a special case" (Gribben, Q is for Quantum). Heisenberg, Werner. Uber quantentheorestische Umdeutung kinematischer und mechanischer Beziehungen. Particle Physics: One Hundred Years of Discoveries: "Foundation of quantum mechanics, Heisenberg approach. Nobel Prize to W. Heisenberg awarded in 1932 'for the creation of quantum mechanics'". Heisenberg; Born, Max and Jordan, Pasqual. Zur Quantenmechanik.Particle Physics: One Hundred Years of Discoveries: "Invention of matrix formalism for the Heisenberg quantum mechanics. Systems with one degree of freedom." Heisenberg, Born, Jordan. Zur Quantenmechanik II. Particle Physics: One Hundred Years of Discoveries: "Development of matrix formalism for the Heisenberg quantum mechanics. Systems with arbitrary many degrees of freedom." IN: Zeitschrift fur Physik, Vols. 33 (pp. 879-893), 34 (858-888), 35 (557-615). Berlin: Julius Springer, 1925-1926. Octavo, volume 33 with half black cloth over marbled boards; volume 34 and 35 in half red cloth over red boards. Volume 33 is taller (wider margins) than the other two volumes. A few institutional stamps to preliminaries. All three volumes with stamps from the prestigious Gmelin Institute (after 1996, part of the Max Planck Institute). Overall, very good condition. Bookseller Inventory # 465

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**Item Description: **FIRST EDITIONS OF THREE LANDMARK PAPERS THAT TOGETHER FORMED THE THEORETICAL FOUNDATION OF QUANTUM MECHANICS. "In spite of its high-sounding name and its successful solutions of numerous problems in atomic physics, quantum theory, and especially the quantum theory of polyelectronic systems, prior to 1925, was, from the methodological point of view, a lamentable hodgepodge of hypotheses, principles, theorems, and computational recipes rather than a logical consistent theory. Every single quantum-theoretic problem had to be solved first in terms of classical physics; its classical solution had then to pass through the mysterious sieve of the quantum conditions or, as it happened in the majority of cases, the classical solution had to be translated into the language of quanta in conformance with the correspondence principle? In short, quantum theory still lacked two essential characteristics of a full-fledged scientific theory, conceptual autonomy and logical consistency" (Jammer, The Conceptual Development of Quantum Mechanics, 196). The work of Heisenberg, Born, and Jordan in these papers began to rectify these issues and together marked the "starting point for the new quantum mechanics," also called matrix mechanics (DSB). "In May 1925, Heisenberg took on a new and difficult problem, the calculation of the line intensities of the hydrogen spectrum. Just as he had done with Kramers and Bohr, Heisenberg began with a Fourier analysis of the electron orbits. When the hydrogen orbit proved too difficult, he turned to the an harmonic oscillator. With a new multiplication rule relating the amplitudes and frequencies of the Fourier components to observed quantities, Heisenberg succeeded in quantizing the equations of motion for this system in close analogy with the classical equations of motion. In June Heisenberg returned to Göttingen, where he drafted his fundamental paper [the first paper offered], which he completed in July. In this paper Heisenberg proclaimed that the quantum mechanics of atoms should contain only relations between experimentally observable quantities. The resulting formalism served as the starting point for the new quantum mechanics, based, as Heisenberg's multiplication rule implied, on the manipulation of ordered sets of data forming a mathematical matrix. Born and his assistant, Pascual Jordan, quickly developed the mathematical content of Heisenberg's work into a consistent theory with the help of abstract matrix algebra [the second paper offered].Their work, in collaboration with Heisenberg, culminated in their "three-man paper" ["Dreimännerarbeit" - the third paper offered] that served as the foundation of matrix mechanics. Confident of the correctness of the new theory, Heisenberg, Pauli, Born, Dirac, and others began applying the difficult mathematical formalism to the solution of lingering problems" (DSB). CONDITION & DETAILS: In: Zeitschrift für Physik 33 (1925), 34 (1925), 35 (1926). 8vo. (9 x 6.25 inches; 225 x 156mm). Three full volumes. All but invisible ex-libris stamp on title pages; no other library markings whatsoever. Handsomely rebound in grey linen, gilt-tooled and lettered at the spine. Tightly and solidly bound. Very clean inside and out. Near fine condition. Bookseller Inventory # 9

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Published by Greenwood Press Reprint (1970)

ISBN 10: 0837131073 ISBN 13: 9780837131078

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**Item Description: **Greenwood Press Reprint, 1970. Hardcover. Book Condition: New. Bookseller Inventory # SONG0837131073

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Published by Berlin : J. Springer (1925)

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**Item Description: **Berlin : J. Springer, 1925. Hardcover. Book Condition: Used: Very Good. 2 Volumes. Band 34 and 37. Bound in modern 3/4 crushed red Moroccan leather. Red cloth boards. TEG. Gilt spine. 5 raised bands. Fine binding and cover. Clean, unmarked pages. Ships daily. Band 34 contains "Uber die physikalischen Konsequenzen der relativistischen Axiomatik" p. 32?48 by Hans Reichenbach and "Zur Quantenmechanik" p. 858-888 by Max Born and Pasqual Jordan. Band 37 contains the first Russian paper on matrix mechanics, "Zur Quantenmechanik des rotators", 685-688 by Igor Tamm, Anwendung der Quantenmechanik auf das Problem der anomalen Zeemaneffekte by Pasqual Jordan; Werner Heisenberg, 263-277 and Zur Quantenmechanik der Stossvorgange by Max Born, 863-867. Max Born's paper would he first to clearly enunciate the probabilistic interpretation of the quantum wavefunction, which had been introduced by Erwin Schrodinger. It would be criticize by Schrodinger but lead to Einstein's quote in a letter "He [God] does not play dice". Bookseller Inventory # 1507150012

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From: Atticus Rare Books (West Branch, IA, U.S.A.)

**Item Description: **FIRST EDITION, FIRST PRINTING of Heisenberg's Uncertainty Principle, one of the most significant discoveries in all of modern physics and "one of the most famous and important aspects of quantum mechanics," (Stanford Encyclopedia of Philosophy).From the moment of publication, the Uncertainty Principle marked the end to deterministic theories of physics and since, has played a critical role in any and allscientific theories or technologies that follow from quantum mechanics. In its simplest form, Heisenberg's Uncertainty Principle, or quantum mechanical principle, states that it is not possible to simultaneously determine the position and momentum of a particle. Moreover, "the more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa" ("Uber den anschaulichen," 1927). This principle applies even to particles that are not interacting with other systems, in other words, that are NOT being "observed." Heisenberg's discoveries punctured the firmly held belief that the universe and everything in it operates like clockwork. To predict the workings of the "clock," one needs to measure its qualities and parts at a specific point in time. Classical physics assumed that the precision of measuring is theoretically unlimited. But Heisenberg stated that since you could never with great certainty measure more than one property of a particle, you could only work with probability and mathematical formulations. This was "the first paper in which the question of what is observable and what is not is quantitatively discussed in the context of quantum mechanics" (Pais, Niels Bohr's Times, 304). The implications of Heisenberg's efforts were extraordinary and in 1932 he received the Nobel Prize.ALSO INCLUDES: Wolfgang Pauli's "Zur Quantenmechanik des magnetischen Elektrons", pp. 601-632. CONDITION & DETAILS: 4to. (9.25 x 6.25 inches; 231 x 156mm). [vii], 936pp. Bound in a bluish, dark grey buckram; very light edge wear to the boards; tightly and very solidly bound. Bears no library markings whatsoever; NOT ex-libris. Minor age toning throughout. There is a barely visible area in the margin of the Heisenberg where at some point, a lightly penciled notation was apparently erased; as said, it is quite difficult to see. Very good condition. Bookseller Inventory # 597

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Published by Julius Springer, Berlin (1926)

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From: Manhattan Rare Book Company, ABAA, ILAB (New York, NY, U.S.A.)

**Item Description: **Julius Springer, Berlin, 1926. Soft cover. Book Condition: Very Good. 1st Edition. FIRST EDITION IN ORIGINAL WRAPPERS of the famous "three-man paper," the first, complete, self-consistent description of quantum mechanics. "In 1925, after an extended visit to Bohr's Institute of Theoretical Physics at the University of Copenhagen, Heisenberg tackled the problem of spectrum intensities of the electron taken as an anharmonic oscillator (a one-dimensional vibrating system). His position that the theory should be based only on observable quantities was central to his paper of July 1925, "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen" ("Quantum-Theoretical Reinterpretation of Kinematic and Mechanical Relations"). Heisenberg's formalism rested upon noncommutative multiplication; Born, together with his new assistant Pascual Jordan, realized that this could be expressed using matrix algebra, which they used in a paper submitted for publication in September as "Zur Quantenmechanik" ("On Quantum Mechanics"). By November, Born, Heisenberg, and Jordan had completed "Zur Quantenmechanik II" ("On Quantum Mechanics II"), colloquially known as the "three-man paper," which is regarded as the foundational document of a new quantum mechanics" (Britannica's Guide to the Nobel Prizes). Particle Physics: One Hundred Years of Discoveries: "Development of matrix formalism for the Heisenberg quantum mechanics. Systems with arbitrary many degrees of freedom." Provenance: With ownership signature on front wrapper of E.F. Barker, noted American physicist who worked primarily at the University of Michigan. IN: Zeitschrift für Physik, Band 35, February 1926, pp. 557-615. Berlin: Julius Springer, 1926. Octavo, original wrappers; custom box. A few creases to wrappers, chips to spine. RARE in original wrappers. Bookseller Inventory # 1276

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Published by Julius Springer, Berlin (1925)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Julius Springer, Berlin, 1925. First edition. A very fine copy (not ex-library) of his breakthrough paper, announcing his discovery of matrix mechanics. "A severe attack of hay fever in early June forced Heisenberg’s retreat to the island of Helgoland. There he completed the calculation of the anharmonic oscillator, determined the constants of motion, and obtained from his multiplication rule the Thomas Kuhn summation rule for spectral lines. After nearly two weeks on Helgoland, Heisenberg returned to Göttingen, where he drafted his fundamental paper 'Über die quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen', which he completed in July. In this paper Heisenberg proclaimed that the quantum mechanics of atoms should contain only relations between experimentally observable quantities. The resulting formalism served as the starting point for the new quantum mechanics, based, as Heisenberg’s multiplication rule implied, on the manipulation of ordered sets of data forming a mathematical matrix." (DSB). In: Zeitschrift für Physik, Vol. 33, pp.879-893. The complete volume offered (VIII,950 pp.) in a nice contemporary half calf binding with gilt spine lettering. Completely clean throughout - a fine copy. Bookseller Inventory # 2911

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Published by Julius Springer, Berlin, 1929-1930

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From: Charles Parkhurst Rare Books, Inc. ABAA (Prescott, AZ, U.S.A.)

**Item Description: **Julius Springer, Berlin, 1929-1930. First Edition. In "Zeitschrift fur Physik" Vol. 56, 1-61pp. and Vol. 59, 168-190pp; bound in blue cloth, spine lettering and call letters gilt; stamp of the Mount Wilson Observatory on front free endpaper, no other library markings. Both volumes are fine and housed in a custom clamshell. These are the only papers on which Heisenberg and Pauli, both Nobel Laureates in Physics (1932 and 1945) collaborated. These are unquestionably important early works in the development of relativistic quantum electrodynamic theory. Bookseller Inventory # pb.0775

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Published by Greenwood Press Reprint (1970)

ISBN 10: 0837131073 ISBN 13: 9780837131078

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**Item Description: **Greenwood Press Reprint, 1970. Hardcover. Book Condition: New. 1St Edition. Bookseller Inventory # DADAX0837131073

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Published by Julius Springer 1929-30, Berlin (1929)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Julius Springer 1929-30, Berlin, 1929. First editions, first printings. A fine set, in the original wrappers, of the two papers in which Heisenberg and Pauli gave "for the first time the foundations for quantum electrodynamics in the way we know it today." (Abraham Pais). "Three years before the discovery of the positron Heisenberg and Pauli – in two papers ‘Zur Quantenmechanik der Wellenfelder’ and ‘Zur Quantenmechanik der Wellenfelder II’ of 29 March and 7 September 1929, respectively – took a decisive step forward to develop a consistent theory of quantum electrodynamics." (Mehra & Milton). "Heisenberg’s foremost scientific concern after 1927 involved the search for a consistent extension of the quantum formalism that would yield a satisfactory unification of quantum mechanics and relativity theory. This required the formulation of a covariant theory of interacting particles and fields that accounted for elementary processes at high energies and small distances. In 1929, drawing upon the work of Dirac, Jordan, Oskar Klein, and others, Heisenberg and Pauli succeeded in formulating a general gauge-invariant relativistic quantum field theory by treating particles and fields as separate entities interacting through the intermediaries of field quanta. "The formalism led to the creation of a relativistic quantum electrodynamics, equivalent to that developed by Dirac, which, despite its puzzling negative energy states, seemed satisfactory at low energies and small orders of interaction. But at high energies, where particles approach closer than their radii, the interaction energy diverged to infinity. Even at rest, a lone electron interacting with its own field seemed to possess an infinite self-energy, much as it did in classical electrodynamics. Attention was directed to the resolution of such difficulties for more than two decades." (DSB under Heisenberg). "Heisenberg and Pauli were well aware of the shortcomings of their theory: the divergence difficulties and the problem of negative energies for the electron. However, the importance of the Heisenberg-Pauli theory cannot be exaggerated; it opened the road to a general theory of quantized fields and thereby prepared the tools, albeit not perfect ones, for the Pauli-Fermi theory of beta-decay and for the meson theories." (Mehra & Milton). Mehra & Milton, Climbing the Mountain: The Scientific Biography of Julian Schwinger, pp. 186-87; Pais, On the Dirac theory of the electron. An annotation, in Werner Heienberg: Collected Works, Vol. AII, pp.95-105. 8vo: 229 x 156 mm. In: Zeitschift für Physik, vol. 56, no. 1-2, pp. 1-61; vol. 59, no. 3-4, pp. 168-90. The two complete issues offered here in the original printed wrappers, some light wear to the spine strip of the first issue and two small pieces missing from the lower left corner (front and rear), otherwise very fine with no stamps or other markings. Rare in such fine condition. A fine set, in the original wrappers, of the two papers in which Heisenberg and Pauli gave "for the first time the foundations for quantum electrodynamics in the way we know it today." (Abraham Pais). "Three years before the discovery of the positron Heisenberg and Pauli – in two papers ‘Zur Quantenmechanik der Wellenfelder’ and ‘Zur Quantenmechanik der Wellenfelder II’ of 29 March and 7 September 1929, respectively – took a decisive step forward to develop a consistent theory of quantum electrodynamics." (Mehra & Milton). "Heisenberg’s foremost scientific concern after 1927 involved the search for a consistent extension of the quantum formalism that would yield a satisfactory unification of quantum mechanics and relativity theory. This required the formulation of a covariant theory of interacting particles and fields that accounted for elementary processes at high energies and small distances. In 1929, drawing upon the work of Dirac, Jordan, Oskar Klein, and others, Heisenberg and Pauli succeeded in formulating a general gauge-invariant relativistic quantum field theory by treating particles and fields as separate entities in. Bookseller Inventory # 2627

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Published by Stuttgart Belser-Presse (1971)

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From: Antiquariat Eckert & Kaun GbR (Bremen, Germany)

**Item Description: **Stuttgart Belser-Presse, 1971. Folio, 79 (3) S., 1 Bl. mit drei Lithographien, Orig.-Leinen m. Orig.-Leinenschuber. Eines von 185 (gesamt 205) nummerierten und vom Künstler im Impressum signierten Exemplaren.- Spies-Leppin 198 D I-II; Spindler, Typen 64.7.- (= Siebenter Druck der Belser-Presse).- Tadelloses Exemplar. Bookseller Inventory # 45711

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From: Jeremy Norman's historyofscience (Novato, CA, U.S.A.)

**Item Description: **1947. Heisenberg, Werner (1901-76). Research in Germany on the technical application of atomic energy. Offprint from Nature 160 (1947). 10, [1]pp. 212 x 145 mm. Without wrappers as issued. Fine copy. First Edition in English, Offprint Issue. During World War II Heisenberg was one of the principal scientists leading research and development in Germany’s nuclear energy program. At that time the Allies had no idea of how far Germany had progressed in the quest to build a nuclear reactor, but given Germany’s leading role in the advancement of nuclear physics they had every reason to believe that the Nazis were ahead of the game—in fact, the fear of a German "atom bomb" was one of the main reasons behind the establishment of the Manhattan Project. This fear turned out to be groundless: Due to a combination of factors, including Hitler’s dislike of "Jewish science" and the "White Jew" Heisenberg, Germany had fallen far behind the United States in the development of nuclear energy. fter the bombing of Hiroshima Heisenberg became one of the primary crafters of Germany’s official account of its wartime nuclear energy program. In December 1946 he published his first postwar summary of the program in the journal Naturwissenschaften; the present English translation, slightly abridged from the German, appeared in Nature the following August. In the summary Heisenberg argued that Germany’s failure to advance its nuclear program was due both to enormous technical difficulties and to the lack of political and financial support; he also played up his own role in slowing down the project by quashing Nazi officials’ hopes for the imminent development of atomic weapons. "Heisenberg’s self-serving account parallels but overinterprets actual events. He especially did try to maintain scientific control over the [nuclear energy] project. He was also aware of the theoretical possibility of a nuclear explosive by late 1941, he did not demand a crash research and development to build one, and he did seem content to work for the rest of the war on the more modest program of building a reactor. It is difficult to assess his intentions and motives beyond that. But from what we know of his activities and research, there is nothing to support the notion that Heisenberg actually hindered the project in any way to keep an explosive out of Hitler’s hands or even that he himself had that much control of the situation" (Cassidy, Uncertainty: The Life and Science of Werner Heisenberg, p. 510). Bookseller Inventory # 43266

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**Item Description: **1925. Kramers-Heisenberg Formula—Stepping Stone to the New Quantum Mechanics Kramers, Hendrik Anthony (1894-1952) and Werner Heisenberg (1901-76). Über die Streuung von Strahlung durch Atome. Offprint from Zeitschrift für Physik 31 (1925). 681-708pp. Original printed wrappers. Light toning, but fine. First Edition, Offprint Issue. During his 1924 visit to Bohr’s Institute for Theoretical Physics in Copenhagen, Heisenberg and Bohr’s assistant H. A. Kramers worked together on the problem of atomic structure from the point of view of dispersion theory. "At first, this interest might appear strange because the problems of atomic structure, say, e.g., the calculation of the energy states of helium, would not seem to have any connection with the scattering of light by atoms, which was the principal concern of dispersion theory. However, Bohr and his collaborators had concluded that the problem of atomic structure could not be separated from the problem of the emission and absorption of radiation—and this could be considered as a problem of the dispersion of radiation" (Mehra & Rechenberg, Historical Development of Quantum Theory, 2, p. 170). Kramers and Heisenberg’s joint paper on the dispersion of light by atoms contained the important Kramers-Heisenberg dispersion formula, an expression of the cross section for scattering of a photon by an atomic electron; among other things, the formula explained the phenomenon of inelastic scattering, anticipating the Raman effect. Heisenberg’s work on this paper "was the final touch needed for [him] to fabricate quantum mechanics six months later" (Cassidy, Uncertainty: The Life and Science of Werner Heisenberg, p. 188). Bookseller Inventory # 43379

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Published by Springer 1943; 1943; 1944, Berlin (1943)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Springer 1943; 1943; 1944, Berlin, 1943. First edition of Heisenberg’s S-matrix approach to the study of elementary particles, complete in three parts (a fourth part was written but not published). Although S-matrix theory was abandoned after the War due to the success of quantum electrodynamics and quantum chromodynamics, it again became very influential in the 1960s when it led to the development of string theory, which is the best-accepted approach to quantum gravity."Heisenberg’s prewar researches in quantum field theory, undertaken in part with Pauli, had led him to the study of cosmic rays, the highest energy particles then available for research. When an extremely high-energy cosmic ray strikes the earth’s atmosphere, it induces a shower of newly created particles and photons. This effect was to be explained on the basis of quantum field theory. Heisenberg’s researches had previously convinced him and others of the inadequacy of field theories for this task. Infinities and divergences plagued all three of the available theories - quantum electrodynamics, Fermi’s theory of beta decay (relating to what is now the weak force), and Yukawa’s meson theory (relating to what is now the strong, or nuclear, force). "The small size of elementary particles and the close approach of the particles to each other in a cosmic ray collision – which triggered the particle shower – indicated to Heisenberg during the 1930s that the difficulties in quantum field theory could be resolved only if a universal minimum length, a new fundamental constant, were introduced into the theory according to Heisenberg, quantum mechanics itself broke down when applied to events occurring within regions smaller than the size of an elementary particle "Pauli had already suggested that Heisenberg, as he did when formulating the 1925 breakthrough in quantum mechanics, should focus only on observable quantities and attempt to exclude all unobservable variables from the theory. Heisenberg now attempted to do so, at the height of the World War. His effort led to what became after the war his widely studied new theory of elementary particles, the so-called S-matrix theory. "In his new approach, Heisenberg used this hypothetical fundamental length to define the allowed changes in the momentum and energy of two colliding high-speed elementary particles. This limitation would help identify the properties of the collision that were observable in present theories. Those at smaller distances were unobservable. For two colliding particles, this yielded four sets of observable quantities with which to work: two of these were the properties of the two particles as seen in the laboratory long before they collide with each other; and two were their properties long after the collision. During the collision they approach within a distance of less than the fundamental length and are thus unobservable. These four sets of observable properties could be arranged in a table, or in this type of work, a matrix, which Heisenberg called the scattering or S-matrix. "Although Heisenberg could not actually specify the four elements of the S-matrix, he demonstrated that it must contain in principle all of the information about the collision. In his second paper, completed in October 1942, Heisenberg further showed that the S-matrix for several simple examples of scattering of particles yielded the observed probabilities for scattering. It also gave the possibility for his favorite phenomenon – the appearance of cosmic-ray explosion showers " one evening in October 1943 Heisenberg presented his new theory to an informal colloquium in Kramers’s home near Leiden in the German-occupied Netherlands During the discussion of Heisenberg’s talk, Kramers made the insightful observation that if the actual elements of the matrix could ever be determined without a complete theory, they would yield a so-called "analytic function" – that is, a function containing real and imaginary parts Back in Berlin, Heisenberg wrote immediately that he. Bookseller Inventory # 3530

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Published by Belser-Presse, Stuttgart (1971)

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From: Des livres autour (Julien Mannoni) (Paris, PARIS, France)

**Item Description: **Belser-Presse, Stuttgart, 1971. Cartonnage Éditeur. Book Condition: Très bon. Max Ernst (illustrator). Ed. originale. In-folio. Stuttgart, Belser-Presse, 1971. 39,5 x 30 cm, in-folio, 79 pp. - 3 lithographies en couleurs hors texte, cartonnage et étui de l'éditeur en pleine toile bise, pièces de titre. Edition originale de cette conférence donnée à l'Académie bavaroise des Beaux-Arts de Munich le 9 juillet 1970. Texte bilingue allemand / anglais. Tirage à 205 exemplaires. Celui-ci l'un des 20 hors commerce, signé au colophon par Max Ernst. Les lithographies ont été tirées par Pierre Chave à Vence. Etui partiellement bruni, quelques infimes rousseurs à la tranche de gouttière. Signé par l'illustrateur. Bookseller Inventory # 1860

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Published by Springer, Berlin (1926)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Springer, Berlin, 1926. First edition of the explanation of the anomalous Zeeman effect on the basis of matrix mechanics. "By including the spin property of the electron, Heisenberg and Jordan obtained perhaps the greatest triumph of matrix mechanics: they were able to derive all observed phenomena connected with the anomalous Zeeman effect" (Rechenberg, p. 211). This paper was of crucial importance in the early history of quantum mechanics because its success in explaining the hitherto mysterious anomalous Zeeman effect validated not only the new quantum mechanics itself but also the highly controversial concept of electron spin, discovered by Uhlenbeck and Goudsmit in the previous year. When an atom is placed in a magnetic field, its spectral lines split into a series of equidistant lines – always an odd number - whose separation is proportional to the field strength. This, the normal Zeeman effect, was explained in 1916 by Debye and Sommerfeld in terms of the ‘old’ quantum theory: the splitting was due to the interaction between the magnetic field and the orbital magnetic moment of the electrons in the atom. However, there is also an anomalous Zeeman effect, observed particularly in atoms with odd atomic number, in which the lines split in a more complex fashion. "During 1920-24, many physicists attacked the problem [of the anomalous Zeeman effect], including Landé, who was able to give a phenomenological explanation of the observed splitting of spectral lines. However, neither Landé, Sommerfeld, Pauli, Heisenberg nor other physicists occupied with the problem could justify their results in terms of quantum theory. "It’s a great misery with the theory of anomalous Zeeman effect," Pauli wrote to Sommerfeld on July 19, 1923" (Kragh, p. 158). After Heisenberg’s introduction of matrix (quantum) mechanics in 1925, one of the first problems he wanted to address using his new theory was the anomalous Zeeman effect. The crucial ingredient was electron spin, which Uhlenbeck and Goudsmit had discovered by studying the regularities in the anomalous Zeeman effect documented by Landé. "Although based originally upon the classical concept of a rotating electron, electron spin is a purely quantum mechanical property intrinsic to the electron. Opinions were strongly divided about the validity of the concept, Pauli taking a strongly negative position, while Bohr, Heisenberg and Jordan took a more positive view. The challenge taken up by Heisenberg was to find a quantum mechanical solution for the anomalous Zeeman effect using the concept of a spin-½ particle within the context of their recently completed matrix formalism. "Despite the less than encouraging views of Pauli, in November 1925 Heisenberg set about [finding] the stationary states and line splittings associated with the anomalous Zeeman effect. Disappointingly, he almost reproduced Landé’s formula for the anomalous Zeeman effect, but the crucial spin-orbit coupling term resulted in a factor of 2 discrepancy from Landé’s expression, a result which cast doubt on the whole scheme. "The solution was, however, at hand thanks to the insight of Llewellyn Thomas who had arrived recently at Bohr’s Institute in Copenhagen as a visiting graduate student Thomas was aware of the fact that there is an additional kinematic effect associated with the orbital motion of a vector, such as the spin vector of the electron, according to the special theory of relativity This purely kinematic effect results in an additional contribution to the precession, and hence interaction energy of the electron and can account completely for the discrepant factor of 2. After considerable debate, even Pauli was convinced and the paper on the quantum mechanical explanation for the anomalous Zeeman effect was published by Heisenberg and Jordan in June 1926. Rechenberg has written in his summary of the history of quanta and quantum mechanics that the explanation of the anomalous Zeeman effect was one of the greatest triumphs of matrix mecha. Bookseller Inventory # 3528

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Published by Julius Springer, Berlin (1922)

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From: SOPHIA RARE BOOKS (Koebenhavn V, Denmark)

**Item Description: **Julius Springer, Berlin, 1922. First edition of Heisenberg’s first published paper, describing his ‘core model’ of the atom and its application to solve the problems of the multiplet structure in atomic spectra and the anomalous Zeeman effect, which had defeated all previous attempts. "Just a year after entering Sommerfeld’s program, Heisenberg amazed his teacher by presenting a model of atoms that seemed to resolve every spectroscopic riddle at a stroke. But the model succeeded only because its daring inventor failed to follow the requirements of an acceptable quantum theory" (Cassidy, Beyond Uncertainty, p. 95). Sommerfeld’s own attempt to solve the same problems precedes Heisenberg’s paper in the same issue."The Bohr theory of atoms and molecules, Sommerfeld’s "quantum theory of spectral lines," and the correspondence principle of 1918 formed the foundations of the Bohr quantum theory. This theory provided in turn the basis for model interpretations of most, but not all, existing phenomena of empirical spectroscopy. Two phenomena, multiplet line spectra and the anomalous Zeeman effect, continually resisted explanation by quantized mechanical models" (Cassidy, pp. 191-192). The eighteen-year-old Heisenberg entered Sommerfeld’s institute in the winter semester of 1920-21, and Sommerfeld immediately introduced him to the Bohr theory. In June 1921 Alfred Landé gave a phenomenological explanation of the splittings observed in the anomalous Zeeman effect, but he did not propose any physical interpretation of his theory, writing to Bohr: "With regard to the complicated types of the Zeeman effect, I have found a few empirical rules which permit one to make predictions regarding the neon spectrum. But what these rules signify is entirely incomprehensible to me." Sommerfeld suggested that Heisenberg should try to find a model to explain Landé’s rules. The result was the present paper, submitted in his third semester, when he was just twenty years old. "In it he claimed that he was presenting the essential details of a complete quantum-theoretical "model interpretation" of the empirical regularities of optical multiplet lines in spectroscopy and the anomalous Zeeman effect of these lines in a magnetic field. All previous attempts to explain these lines by mechanical models had failed The model was nevertheless riddled with what Max Born called "conscious deviations" from accepted principles and procedures. "Heisenberg, Sommerfeld’s "vastly gifted pupil," had reduced the previously inexplicable line structure to internal magnetic interactions between the valence electrons and the rest of the atom. The inner orbits and nucleus acted as a solid core possessing on the average a half-unit of angular momentum. Half-integral quantum numbers and magnetic interactions between orbital interactions between orbital electrons had already appeared in the work of Landé and others, but half-integral momenta and a magnetic core had not. They could not be justified in either classical or quantum theory, despite Sommerfeld’s blessing. "Although the model was theoretically untenable, with it Heisenberg could quantitatively account for doublet and triplet term energies. By attributing half-integral angular momenta to the valence electrons, he could also derive the semi-empirical Landé g-factors for the anomalous Zeeman effect and their continuous transition to unity in the Paschen-Back effect. "Heisenberg’s accomplishments were unique, but Bohr judged his "interesting paper" to be "hardly agreeable with the general assumptions" of quantum theory. Not only had Heisenberg introduced real non-integral momenta, but he had also violated the Sommerfeld quantum conditions, classical radiation theory, the Larmor precession theorem, and the semi-classical criterion of perceptual clarity (Anschaulichkeit) in model interpretations. The impact of these violations upon the rational advance of quantum theory spurred Bohr and others to try to derive Heisenberg’s results without straying too far f. Bookseller Inventory # 3527

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Published by Springer-Verlag, Berlin, Heidelberg, New York (1985)

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**Hardcover**
**First Edition**

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From: Secret Knowledge Books (Tualatin, OR, U.S.A.)

**Item Description: **Springer-Verlag, Berlin, Heidelberg, New York, 1985. Hard Cover. Book Condition: Very Good. Dust Jacket Condition: Very Good. First Edition. 8vo - over 7? - 9? tall. 4 thick oversize volumes, XI, 633 pp; X, 717 pp; X, 700 pp; X, 937 pp. cloth hardcover with dustjacket, Heisenberg's complete published scientific papers, reproduced in facsimile, including several top secret papers on the Nazi nuclear project. Text in German and English. Slight un-evenness of the bookblock of serie A vols 2 and 3. A very good set, not ex-library copy. 8vo - over 7? - 9? tall. Bookseller Inventory # 001583

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Published by Springer-Verlag (1993)

ISBN 10: 038713848X ISBN 13: 9780387138480

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**Hardcover**

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From: Irish Booksellers (Rumford, ME, U.S.A.)

**Item Description: **Springer-Verlag, 1993. Hardcover. Book Condition: New. book. Bookseller Inventory # 038713848X

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**Used**

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From: Atticus Rare Books (West Branch, IA, U.S.A.)

**Item Description: **FIRST EDITION, FIRST ISSUE OF TWO SEMINAL PAPERS: Heisenberg's groundbreaking contribution to magnetism and to the identification of the quantum mechanical exchange energy. "Heisenberg's masterly contribution in magnetism lies in identifying the quantum mechanical exchange energy, first appearing in the context of chemical bonding and spectroscopy, to be of central importance in explaining ferromagnetism? The question was this: If every atom has an outer cloud of electrons, then how do atoms approach each other to form a chemical bond? It was Heisenberg who showed that the interaction between electrons, called the exchange energy," was the key (ibid., 60). His "exchange interaction" is a force generated solely by the exchange of positions of two totally indistinguishable quantum particles - "a quantum mechanical effect which increases or decreases the expectation value of the energy or distance between two or more identical particles when their wave functions overlap" (Wikipedia). In the early 20th century physicists did not understand ferromagnetism on an atomic basis. "It was Heisenberg's work in the late 1920's that filled this void. To accomplish this, quantum mechanics had to be discovered first? It was indeed in the fitness of things that the quantum dynamics of the electron left an imprint on another area, namely magnetism, which too had to do with the magnetic effects of electron dynamics" (ibid., 58). What Heisenberg began to understand was the connection between ferromagnetism and electron bonding, two areas that most physicists believed were wholly unconnected phenomena. "It was Heisenberg, who saw the connection and established it in two seminal papers, written in 1926 and 1928 [the two papers offered here]" (Chatterjee, "Heisenberg and Ferromagnetism," Resonance, 2004, 63-64). CONDITION & DETAILS: Berlin: Julius Springer. 4to. (9 x 6.5 inches; 225 x 163mm). Two full volumes. Zeitschrift für Physik Volumes 39 and 49. Handsomely bound in black cloth over marbled paper boards; library labels removed with slight ghosting visible. Very minor rubbing at the edges on Volume 39. Both tightly and solidly bound. Near pristine throughout the interior. Bookseller Inventory # 217

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Published by Zeitschrift fur physik, 1 2-1933, In: (1933)

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**First Edition**

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From: Jeff Weber Rare Books, ABAA (Carlsbad, CA, U.S.A.)

**Item Description: **Zeitschrift fur physik, 1 2-1933, In:, 1933. hardcover. 1 FIRST EDITION of the final mathematical model of the atom. After Chadwick had discovered the neutron, Heisenberg was the FIRST TO STATE THAT THIS DISCOVERY ELIMINATED THE NEED FOR ASSUMING THE PRESENCE OF ELECTRONS IN THE NUCLEUS OF AN ATOM. Bohr and Heisenberg received word of Chadwick's discovery of the neutron in the middle of March 1932. Within three months of hearing of the neutron, Heisenberg succeeded in using it as the basis of a semiquantitative explanation of the composition and stability of nuclei. The discovery of the neutron made it possible to change the relation between nuclear physics and the domain of unsolved problems. A substantial number of nuclear problems now became solvable by ordinary quantum mechanics. The achievement of Heisenberg was to see this possibility and find a way to give it formal expression. "Three papers by Heisenberg completed in the latter half of 1932 mark the transition to the modern view on nuclear forces. These articles, important though they are, must not be considered as a clean break with the past, however. Heisenberg's nuclear theory is a hybrid of the old and the new. It has the virtue of being based on the proton-neutron model of the nucleus, but the drawback of a proton-electron model for the neutron. The key to understanding Heisenberg's 1932 papers is simply this: at that time he sided with Bohr." Pais, Inward bound. Bromberg, The impact of the neutron; Hahn, Autobiography, p. 272; Pais, Inward bound, p. 413. Three volumes. 8vo. 77, (1932), pp. 1-11; 78 (1932), pp. 156-64; 80 (1933), pp. 587-596. Navy cloth, gilt stamped spine. Ex library Carnegie Institution of Washington Mount Wilson Observatory with call number gilt stamped on spine and library blind-stamp on front free end paper. Clean copy, handsomely bound; covers lightly freckled, else fine. RARE. Bookseller Inventory # S0439

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From: Atticus Rare Books (West Branch, IA, U.S.A.)

**Item Description: **First editions of the three papers in which heisenberg formulated the final mathematical model of the atom -- the neutron-proton model for the atomic nucleus - and the papers in which he introduced the concept of nucleon isotropic spin (later named "isospin"). The books bear the stamp of Friedrich Hermann Hund, a German physicist well-known for his work on atoms and molecules. "After Chadwick had discovered the neutron, Heisenberg was the first to state that this discovery eliminated the need for assuming the presence of electrons in the nucleus of an atom" (Pais). Chadwick's discovery "made it possible to change the relation between nuclear physics and the domain of unsolved problems. A substantial number of nuclear problems now became solvable by ordinary quantum mechanics" (ibid). Still, "once it was accepted that the nucleus was composed of protons and neutrons and that quantum mechanics could be applied to it, the question remained which force acted between its constituents. Heisenberg assumed it to be an exchange force, i.e., a force based on the symmetry properties of a quantum-mechanical wave function" (Brandt, The Harvest of the Century, pp. 223-224). Only a few months after Chadwick's discovery, Heisenberg used Chadwick's neutron to construct the first quantum mechanical nuclear model. The main mechanism he proposed was an exchange force produced by protons and neutrons passing electrons around like basketball players tossing a ball" (Peacock, The Quantum Revolution, 94). Heisenberg postulated that the proton and neutron were two states of the same particle, the nucleon, differing only in isospin. In his theory, the nuclear force conserved isospin, which accounted for the similarities between protons and neutrons. Other forces, such as electromagnetism, broke isospin symmetry, which explained the nucleons' differences. Heisenberg was wrong about the nature of the proton and neutron, but was correct about the importance of isospin in the weak nuclear force. Heisenberg's theory was "quantitatively insufficient to explain nuclear forces. [and] the riddle of nuclear forces stayed a subject of research for decades to come. The lasting value of Heisenberg's approach lies in the revelation of inner symmetries of elementary particles and of quantum numbers associated with these symmetries. The discovery of further symmetries of this type would lead first to a classification of particles and then to an understanding of the forces between them" (Brandt, 226). CONDITION & DETAILS: In: Zeitschrift für Physik 77 (1932), 78 (1932), 80 (1933). Berlin: Julius Springer. 8vo. (9 x 6.5; 225 x 163mm). Three full volumes. The books bear the stamp (on ffp) of Friedrich Hermann Hund, a physicist well-known for his work on atoms and molecules. Friedrich Hermann Hund "was a German physicist from Karlsruhe known for his work on atoms and molecules. Hund worked with such prestigious physicists as Schrödinger, Dirac, Heisenberg, Max Born, and Walter Bothe. He published more than 250 papers and essays in total. Hund made pivotal contributions to quantum theory - especially concerning the structure of the atom and of molecular spectra" (Wikipedia). The set is also ex-libris with very, very slight 'ghosting' from the removal of spine labels. Small stamp appears on the rear of the title pages. Bound in black cloth over marbled paper hardboard. Very slightly rubbed at the edges. Tightly bound and very clean. The interior is clean and bright. Very good + condition. Bookseller Inventory # 11

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From: Michael R. Thompson Books, A.B.A.A. (Los Angeles, CA, U.S.A.)

**Item Description: **All attempts to explain the helium spectra using the old quantum mechanics of Bohr and Sommerfeld had failed. Incorporating both Pauli's exclusion principle and spin into Schršdinger's two-electron wave function, Heisenberg was finally able to derive a good approximation to the emission spectrum of helium. This result marks the second great triumph of wave mechanics after Schršdinger;s treatment of hydrogen. In the course of this derivation, Heisenberg hit upon a new insight and established the principle of "exchange interaction"Ña force generated solely by the exchange of positions of two totally indistinguishable quantum particlesÑwhich turned out to have much wider implications in both solid-state and nuclear physics. Van Vleck won the 1977 Nobel Prize in physics for his "fundamental theoretical investigations of the electronic structure of magnetic and disordered systems." Octavo. Contemporary blue buckram, with title, issue, and year in gilt on spine. Very good. With the pencil signature of Nobel Laureate John H. Van Vleck. Bookseller Inventory # 7984

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Published by Springer-verlag (1989)

ISBN 10: 0387138471 ISBN 13: 9780387138473

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**Hardcover**
**First Edition**

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From: Delhi Book Store (new delhi, Del, India)

**Item Description: **Springer-verlag, 1989. Hardcover. Book Condition: Like New. 1st. Bookseller Inventory # 0387138471

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Published by Berlin: Julius Springer, 1928. (1928)

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**First Edition**

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From: Michael R. Thompson Books, A.B.A.A. (Los Angeles, CA, U.S.A.)

**Item Description: **Berlin: Julius Springer, 1928., 1928. Heisenberg's paper resolved the puzzle of magnetism in iron, which he developed independently of the quantum mechanical explanation of the nature of ferromagnetism offered that year by Yakov Frenkel (DSB, V, p. 160). First edition. Bookseller Inventory # 7985

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Published by Harper Torchbooks, Harper & Row, Publishers (1975)

ISBN 10: 0061318590 ISBN 13: 9780061318597

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From: Nearfine Books (Brooklyn, NY, U.S.A.)

**Item Description: **Harper Torchbooks, Harper & Row, Publishers, 1975. Book Condition: very good. Gently used. Expect delivery in 2-3 weeks. Bookseller Inventory # 9780061318597-3

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Published by 0

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**Signed**

Quantity Available: 1

From: Antiquariat Luna GbR (Lüneburg, Germany)

**Item Description: **0. Kein Einband. Book Condition: Gut. Porträt - s/w Foto signiert von dem deutschen Wissenschaftler und Physik- Nobelpreisträger Werner Heisenberg (1901-76) .Werner Heisenberg erhielt 1932 den Nobelpreis für Physik. photo signed by Werner Heisenberg Size: 16,5x12 cm. Vom Wissenschaftler signiert. Buch. Bookseller Inventory # 010750

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Published by Springer Verlag

ISBN 10: 0387138471 ISBN 13: 9780387138473

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From: Nauka Japan LLC (Tokyo, ., Japan)

**Item Description: **Springer Verlag. Hardcover. Book Condition: New. 0387138471. Bookseller Inventory # NJ001696

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