Self-adjoint extensions and spectral analysis in the generalized Kratzer problem
| Autor: | Baldiotti, M. C., Gitman, D. M., Tyutin, I. V., Voronov, B. L. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Phys. Scr., 83 065007 (2011) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/0031-8949/83/06/065007 |
| Popis: | 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. Comment: 31 pages, 1 figure |
| Databáze: | arXiv |
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