Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method

TL;DR

This paper analyzes the bound states of an isotonic oscillator potential using the Nikiforov-Uvarov method, providing explicit solutions for both nonrelativistic and relativistic cases, including energy spectra and wave functions.

Contribution

It offers new analytical solutions for the isotonic oscillator in both nonrelativistic and relativistic regimes using the Nikiforov-Uvarov method.

Findings

Explicit nonrelativistic energy spectrum and wave functions derived.

Analytic eigenvalues and spinor solutions for the Dirac equation obtained.

Solutions expressed in terms of associated Laguerre polynomials.

Abstract

A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the non-relativistic bound state energy spectrum E_{n} and the wave functions {\psi}_{n}(x) in terms of the associated Laguerre polynomials in the framework of the Nikiforov-Uvarov method. Under the spin and pseudospin symmetric limits, the analytic eigenvalues and the corresponding two-component upper- and lower-spinors of the Dirac particle are obtained, in closed form.