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

2012/03/31 by Sameer M. Ikhdair, Ramazan Sever
Physics and Astronomy · Mathematics · #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.3671640

published as J. Math. Phys. 52 (2011) 122108 · 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:0711.4899

arxiv created 2012/04/13 · arxiv updated 2012/04/16

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 ψ_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.

Citations

• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator