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A new approach to solve the Schrodinger equation with an anharmonic sextic potential

Abstract

In this study, the N-dimensional radial Schrodinger equation with an anharmonic sextic potential is solved by the extended Nikirov-Uranov method. We prove that the radial function can be factorised as the product between an exponential function and a polynomial function solution of the biconfluent Heun equation. The approach investigated in this article aims to be an alternative to other known methods of solving, as it has the advantage of dealing with simple, first-order differential and algebraic equations and avoiding numerous and laborious coordinate transformations and series expansions.

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The author declares no affiliation or involvement with any organisation or entity with any financial interest (e.g. honoraria, educational grants, participation in speakers’ bureaus; membership, employment, consultancy, stock ownership or other equity interest; and expert testimony or patent-licensing arrangements) or non-financial interest (e.g. personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

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Correspondence to Luca Nanni.

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Nanni, L. A new approach to solve the Schrodinger equation with an anharmonic sextic potential. J Math Chem 59, 2284–2293 (2021). https://doi.org/10.1007/s10910-021-01289-5

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Keywords

  • Polynomial potential
  • Nikirov-Uranov formalism
  • Hypergeometric equation
  • Schrodinger equation

Mathematics Subject Classification

  • Primary: 26C05
  • 34K21
  • Secondary: 33C15