13 July 2004 Separable potentials as a bridge between continuous and discrete scattering theories
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Abstract
A special class of separable potentials in the momentum space is proposed which is equivalent to 3D δ-functions in the configuration space. These potentials allow generation of a large number of exact solutions of time-dependent and time-independent Helmgoltz (Schroedinger) equations. It is shown numerically that in the 1D case δ-functions effectively approach the continuous potentials via a convergent algorithm.
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V. V. Sokolovsky, Yuri V. Popov, A. A. Gusev, Sergey I. Vinitsky, "Separable potentials as a bridge between continuous and discrete scattering theories", Proc. SPIE 5476, Saratov Fall Meeting 2003: Laser Physics and Photonics, Spectroscopy, and Molecular Modeling IV, (13 July 2004); doi: 10.1117/12.578892; https://doi.org/10.1117/12.578892
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