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.
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Kukulin, V.I., Rubtsova, O.A. Discrete Quantum Scattering Theory. Theoretical and Mathematical Physics 134, 404–426 (2003). https://doi.org/10.1023/A:1022657607306
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DOI: https://doi.org/10.1023/A:1022657607306