Construction of potential functions associated with a given energy spectrum
Quantum Physics
2020-07-09 v1 Mathematical Physics
math.MP
Abstract
Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy spectrum. In this work, we study the class of problems with a mix of continuous and discrete energy spectrum that are associated with the continuous dual Hahn polynomial. These include the one-dimensional logarithmic potential and the three-dimensional Coulomb plus linear potential.
Keywords
Cite
@article{arxiv.2002.03803,
title = {Construction of potential functions associated with a given energy spectrum},
author = {A. D. Alhaidari},
journal= {arXiv preprint arXiv:2002.03803},
year = {2020}
}
Comments
18 pages, 3 Tables, 4 Figures