Abstract
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself.
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References
Reed, M., Simon, B.: Methods of Modern Mathematical Physics III: Scattering Theory. Academic Press, New York (1979) (The best comprehensive modern textbook on the mathematics of single-channel scattering theory, in the time-dependent operator approach emphasized in this book. It is essentially a book inspired by a physical problem, but nevertheless a pure mathematics book. Note : The quote at the front of this chapter is from page ix of this book and is reprinted here with kind permission of Elsevier.)
Hunziker, W., Sigal, I.M.: Time-dependent scattering theory of N-body quantum systems. Rev. Math. Phys. 12, 1033–1084 (2000)
Taylor, J.R.: Scattering Theory: The Quantum Theory of Nonrelativistic Collisions. Dover (2006) (This book gives a full discussion both of time-dependent and time-independent scattering theory; it explains in particular the precise relation between the two. It also has a chapter in which multi-channel scattering is clearly explained. In a certain way it is the opposite of the book of Reed and Simon: a physics book with great attention for the mathematical background.)
Faddeev, L.D., Merkuriev, S.P.: Quantum Scattering Theory for Several Particle Systems. Translated from the 1985 Russian Edition. Springer 1993, paperback edition 2010 (A basic reference for the scattering of many particle systems. Faddeev’s work laid the basis of the mathematical theory of multi-channel scattering.)
Kato, T.: Fundamental properties of hamiltonian operators of: Schrödinger Type. Trans. Amer. Math. Soc. 70, 195–211 (1951)
Kato, T.: Perturbation Theory for Linear Operators. Springer (1966), Reprint Edition 1995 (After almost 50 years still the basic reference for the subject.)
Dollard, J.D.: Quantum-mechanical scattering theory for short-range and Coulomb interactions. Rocky Mt. J. Math. 1, 5–88 (1971). http://projecteuclid.org/download/pdf_1/euclid.rmjm/1250131999, An errata at: http://projecteuclid.org/download/pdf_1/euclid.rmjm/1250187234 (In addition to its treatment of the generalized scattering formalism needed for the Coulomb potential, this paper can be recommended as a general introduction to time-dependent scattering theory for a nonrelativistic particle in a given potential, which is both clear and rigorous.)
Dollard, J.D.: Asymptotic convergence and Coulomb interactions. J. Math. Phys. 5, 729–738 (1964)
Teschl, G.: Mathematical Methods in Quantum Mechanics With Applications to Schrödinger Operators. American Mathematical Society, Providence (2009)
Newton, R.G.: Scattering Theory of Waves and Particles, McGraw-Hill, 1966. 2nd edition, Dover 2013 (A very comprehensive (768 pages) textbook on all aspects of classical and quantum scattering theory, but mainly in the time-independent formulation.)
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Bongaarts, P. (2015). Scattering Theory. In: Quantum Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-09561-5_14
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DOI: https://doi.org/10.1007/978-3-319-09561-5_14
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