Asymptotic behavior of the wave function of a system of several particles with pair interactions increasing at infinity

E. A. Yarevskii

Saint Petersburg State University, Saint Petersburg, Russia

Abstract: We construct an asymptotic representation of the wave functions of systems of two and three quantum particles with pair interactions increasing at infinity. We consider three-particle systems on the line and in the three-dimensional space. The eikonal and transport equations used to construct the asymptotic representation differ significantly from the corresponding equations in the case of decreasing potentials. We study the solution of the nonlinear eikonal equation in detail.

Keywords: confinement, eikonal equation, asymptotic behavior of wave function.

DOI: 10.4213/tmf8976

 English version: Theoretical and Mathematical Physics, 2016, 186:1, 136–146

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