Construction of potential functions associated with a given energy spectrum
arXiv:2002.03803 · doi:10.1142/S0217751X20501043
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.
arXiv comment18 pages, 3 Tables, 4 Figures
References in corpus (6)
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- The Wilson-Racah Quantum System
- Quantum mechanics with orthogonal polynomials
- The Hahn Quantum System