This article is cited in 15 papers

Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)

V. I. Kukulin, O. A. Rubtsova

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: Constructing the basic operators of scattering theory on and off the mass shell in terms of spatially bounded stationary wave packets or proper differentials is described. For this, we use a technique based on a certain scheme for discretizing the continuum. Finite-dimensional approximations for the Green's functions and $T$-matrix, which are first found here, are immediately constructed for any energy using a single simple diagonalization of the Hamiltonian matrix in an $L_2$-type complete basis. We show that the developed approach leads to a convenient finite-dimensional representation of the scattering operators in the basis of the wave functions of a harmonic oscillator. The method allows an immediate extension to the problem of three and more bodies.

Received: 23.05.2001

DOI: 10.4213/tmf291

 English version: Theoretical and Mathematical Physics, 2002, 130:1, 54–73

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