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 fieldFor g2 > 0 and g1 < 0, the potential is known as the Kratzer potential VK (x) and is usually used to describe molecular energy and structure, interactions between different molecules, and interactions between nonbonded atoms.We construct all self-adjoint Schrödinger 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.

Localization effect on Rényi complexity of Kratzer potential in the presence of Aharonov‐Bohm field

“…[ 2 ] The ring‐shaped Kratzer potential has been used to determine the noncentral ro‐vibrational energies and wave functions. In this article, we introduce the scalar potential as a sum of the Kratzer potential [ 1–40 ] and a θ ‐dependent potential V 1 ( θ ) in the form where D e , r , and r e are respectively the dissociation energy, the internuclear distance, and the equilibrium intermolecular separation between two diatomic molecules, and the Aharonov‐Bohm (AB) flux field [ 41–50 ] as a vector potential takes the form where ℱ is the flux created within a very thin and infinitely long solenoid along the z direction. [ 41,42 ] is called the flux quantum number, such that .…”

“…The ring‐shaped Kratzer potential has applications in ring‐shaped organic molecules such as cyclic polyenes and benzene. [ 6,9 ] In the field of quantum chemistry, we have found many papers of radial Kratzer [ 3,7,8,19,25,26,28,32–39 ] and single or double ring‐shaped Kratzer [ 11–17,27 ] potential in three dimensions [ 4,20,22–24,40 ] and multidimensions. [ 5,18,21,29–31 ] The exact solutions and spectrum analysis of the radial Schrödinger equation for Kratzer potential have been carried out a few years ago in the absence of the AB field.…”

Об Изоморфизме Одно- И Двумерных Осцилляторных И Кулоноподобных Теорий

“…Эта задача является частным случаем обобщенной проблемы Кратцера, которая была решена в работе [7] (см. также работы [9], [10]). Здесь мы приведем результаты, которые нужны для сравнения спектров дуальных теорий.…”

“…также работы [9], [10]). Мы приведем полученные в этих работах результаты в форме, ко-торая позволит сравнить спектры и собственные функции дуальных теорий.…”

Analysis of nonrelativistic particles in noncommutative phase-space under new scalar and vector interaction terms

“…Now in this paper, we study a nonrelativistic particle in NCPS in the presence of an external magnetic field for a combination of linear and quadratic terms plus scalar and vector Kratzer potentials. This potential is a generalization of Cornell, Killingbeck, and Kratzer-type interactions and it is used to describe the atomic, molecular structure and thus plays an important role in quantum calculations [31][32][33][34]. It is also one of the rare potentials of quantum systems which is exactly solvable.…”