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

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.

arXiv comment15 pages, 4 figures. arXiv admin note: text overlap with arXiv:0711.4899

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