Estimation of the imaginary part of the scattering matrix pole for the three-dimensional Schrödinger equation with a trap potential

A. A. Arsen'ev

M. V. Lomonosov Moscow State University

Abstract: A method is proposed for estimating the imaginary part of the scattering matrix resonant pole for the three-dimensional Schrödinger equation with a trap potential. The method is based on the invariance of the wave operators and on the Parseval equality. It is shown that as the barrier height increases, the imaginary part of the scattering matrix resonant pole exponentially tends to zero.

Received: 11.09.1997

DOI: 10.4213/tmf839

 English version: Theoretical and Mathematical Physics, 1998, 114:2, 215–219

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