Construction of potential functions associated with a given energy spectrum

• URL: http://arxiv.org/abs/2002.03803v1
• Date: Wed, 5 Feb 2020 14:30:26 GMT
• Title: Construction of potential functions associated with a given energy spectrum
• Authors: A. D. Alhaidari
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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