This article is cited in 16 papers

Discrete Quantum Scattering Theory

V. I. Kukulin, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: 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, $T$-matrix, discretization of continuum.

Received: 11.03.2002

DOI: 10.4213/tmf165

 English version: Theoretical and Mathematical Physics, 2003, 134:3, 404–426

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