Synopsis
This book presents the formal theory of collision and reaction processes, offering a detailed mathematical treatment of quantum transitions occurring in a system under a perturbation, with a focus on instances where the energy of an incident particle is close to that with which the particle could be bound. In this scenario, resonance phenomena can significantly impact the outcome, and this book delves into their intricacies. The treatment begins with a discussion of the unperturbed Hamiltonian's spectrum, with separate considerations for discrete and continuous spectra. The author then introduces a perturbation and constructs the resolvent operator, which serves as a pivotal quantity in the theory, providing insights into the system's response to external influences. Various matrix elements of the resolvent operator are derived for both discrete and mixed spectra, facilitating the calculation of transition amplitudes. Asymptotic formulas are obtained for large values of time, revealing the long-term behavior of the system. The book concludes by demonstrating how these results can be applied to the time-dependent Schrödinger equation, showcasing the theory's practical applications. Overall, this book provides a comprehensive and rigorous foundation for understanding the formal theory of collision and reaction processes, particularly in cases involving resonance phenomena, making it a valuable resource for physicists and mathematicians working in these areas.
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On the Formal Theory of Collision and Reaction Processes (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book presents the formal theory of collision and reaction processes, offering a detailed mathematical treatment of quantum transitions occurring in a system under a perturbation, with a focus on instances where the energy of an incident particle is close to that with which the particle could be bound. In this scenario, resonance phenomena can significantly impact the outcome, and this book delves into their intricacies. The treatment begins with a discussion of the unperturbed Hamiltonian's spectrum, with separate considerations for discrete and continuous spectra. The author then introduces a perturbation and constructs the resolvent operator, which serves as a pivotal quantity in the theory, providing insights into the system's response to external influences. Various matrix elements of the resolvent operator are derived for both discrete and mixed spectra, facilitating the calculation of transition amplitudes. Asymptotic formulas are obtained for large values of time, revealing the long-term behavior of the system. The book concludes by demonstrating how these results can be applied to the time-dependent Schrà dinger equation, showcasing the theory's practical applications. Overall, this book provides a comprehensive and rigorous foundation for understanding the formal theory of collision and reaction processes, particularly in cases involving resonance phenomena, making it a valuable resource for physicists and mathematicians working in these areas. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332172740_0
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On the Formal Theory of Collision and Reaction Processes (Classic Reprint)
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332172740
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