The Nikiforov-Uvarov method
Guillermo Gordillo-N\'u\~nez
TL;DR
This paper reviews the Nikiforov-Uvarov method, a technique for solving eigenvalue problems in quantum mechanics, focusing on spectral characterization and applications to specific potentials.
Contribution
It provides a comprehensive overview of the Nikiforov-Uvarov method and demonstrates its application to quantum eigenvalue problems involving various potentials.
Findings
Effective spectral characterization of quantum eigenvalue problems
Solutions for specific quantum potentials
Connection between orthogonal polynomials and quantum spectra
Abstract
We review the so-called Nikiforov-Uvarov method along with some basic results about classical orthogonal polynomials and hypergeometric functions related to the hypergeometric differential equation. The method is employed to address certain eigenvalue problems that appear in quantum mechanics, namely, time-independent Schr\"odinger equation, paying special attention to properly and completely characterising its spectrum. Finally, some potentials are discussed and solved.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Matrix Theory and Algorithms