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

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.

31 pages, 1 figure

References in corpus (2)

• Dirac Hamiltonian with superstrong Coulomb field
• Self-adjoint extensions and spectral analysis in Calogero problem

Cited by in corpus (3)

• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Observables in Quantum Mechanics and the Importance of Self-adjointness
• About dual one-dimensional oscillator and Coulomb-like theories