1203.1736 (Sameer M. Ikhdair et al.)

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

Sameer M. Ikhdair, R. Sever

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.

View original: http://arxiv.org/abs/1203.1736