Geodesic
Discrete Quantum Scattering Theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 460-486

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We formulate quantum scattering theory in terms of a discrete $L_2$-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: $S$- and $T$-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann–Schwinger equations for the $T$-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators.
Keywords: quantum scattering theory, wave packets, Green's function, wave operator, discretization of continuum.
Mots-clés : $T$-matrix 
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     author = {V. I. Kukulin and O. A. Rubtsova},
     title = {Discrete {Quantum} {Scattering} {Theory}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {134},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a10/}
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V. I. Kukulin; O. A. Rubtsova. Discrete Quantum Scattering Theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 460-486. http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a10/