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arXiv · 1009.4903

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

M. C. Baldiotti·D. M. Gitman·I. V. Tyutin·B. L. Voronov
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Abstract

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the Kratzer potential and is usually used to describe molecular energy and structure, interactions between different molecules, and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential $V(x)$ and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving spectral problems, we follow the Krein's method of guiding functionals. This work is a continuation of our previous works devoted to Coulomb, Calogero, and Aharonov-Bohm potentials.

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M. C. Baldiotti, D. M. Gitman, I. V. Tyutin, B. L. Voronov. 2010-09-24. Self-adjoint extensions and spectral analysis in the generalized Kratzer problem. https://doi.org/10.1088/0031-8949%2F83%2F06%2F065007

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