Series solutions of Bessel-type differential equation in terms of orthogonal polynomials and physical applications

• URL: http://arxiv.org/abs/2006.13821v1
• Date: Tue, 23 Jun 2020 11:56:26 GMT
• Title: Series solutions of Bessel-type differential equation in terms of orthogonal polynomials and physical applications
• Authors: A. D. Alhaidari and H. Bahlouli
• Abstract summary: We obtain a class of exact solutions of a Bessel-type differential equation. We use our findings to obtain solutions of the Schr"odinger equation for some novel potential functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We obtain a class of exact solutions of a Bessel-type differential equation, which is a six-parameter linear ordinary differential equation of the second order with irregular (essential) singularity at the origin. The solutions are obtained using the Tridiagonal Representation Approach (TRA) as bounded series of square integrable functions written in terms of the Bessel polynomial on the real line. The expansion coefficients of the series are orthogonal polynomials in the equation parameters space. We use our findings to obtain solutions of the Schr\"odinger equation for some novel potential functions.

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