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BOUND FIRST EDITION OF SLATER'S 1928 SUGGESTION FOR SOLVING THE THREE-BODY PROBLEM FOR ATOMS CONTAINING MULTIPLE ELECTRONS. The Schrödinger equation presented the world with â??the three-body problem' - "the state of motion cannot be solved analytically for systems in which three or more distinct masses interact" (Tsuneda, Hartree-Fock Method, 35). Two years after Schrödinger's publication, Hartree presented the Hartree method, a method that solved the equation for multiple-electron systems based on fundamental physical problems. Immediately following Hartree's publication, Slater, while on the faculty at Harvard, made a study of its accuracy. In the American physicist John Clarke Slater's 1928 abstract, he says as much: "The method proposed by Hartree for the solution of problems in atomic structure is examined as to its accuracy as a method of solving Schrödinger's equation" (Slater, 1928, 339). Slater believed that the first step in discussing Hartree's method is to formulate his process mathematically - and he proceeded to do so. "He assumed the many-electron wave function was a product of one electron functions and studied how well this product satisfied Schrödinger's equations" (Fischer, Hartree's Life in Science and Computing, 47). Slater's analysis "showed that the Hartree equations (and energies) should be corrected slightly, because the distributions were not always spherically symmetric. He went on to show that the estimated size of the corrections was of the order of the errors present in the numerical cases he worked" (ibid). As a result, then, of Slater's work, by the end of 1928 Hartree's method was placed on a firm mathematical foundation. A wave function is set up at once from his method, and the matrix of the energy computed with respect to it. The non-diagonal terms are shown to be small, indicating that the function is a good approximation to a real solution. The energy levels are found by perturbation theory from this matrix, and are compared with the term values as found by Hartree. His values should be corrected for three reasons: he has neglected the fact that electron distributions are not really spherical; he has not considered the resonant interactions between electrons; and he has made an approximation which amounts to neglecting the polarization energy. The sizes of these corrections are estimated, and they are found to be of the order of the errors actually present in the numerical cases he has worked out" (Slater, 1928, 339). ALSO INCLUDED: Mulliken's "The Assignment of Quantum Numbers for Electrons in Molecules. II. Correlation of Molecular and Atomic Electron States". "To find out the possible quantum numbers for each electron in the molecule, Mulliken suggests [in this paper] that they were obtained from those of the associated united atoms by placing them in a strong axially symmetrical electric field, so that the two resulting nuclei were fixed. Several coupling schemes could be applied and, contrary to what happened in the atomic case, in molecules there was no limiting case, and â??the actual condition usually lies more or less in the midst of a region between several limiting cases" (Mulliken, 1928, 191-192). CONDITION & DETAILS: Minneapolis: Physical Review. Complete volume. (10 x 7; 250 x 150mm). Ex-libris, pictorial bookplate on the front pastedown; small stamp on front and rear flyleaves; perforated stamp on title page. Solidly and tightly bound in brown buckram; gilt-lettered at the spine. The interior is bright and clean throughout. Very good condition.
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