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Relativistic and Nonrelativistic Bound States of the Isotonic Oscillator by Nikiforov-Uvarov Method

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Tue, 2013-09-10 13:18 — Sameer. Ikhdair
Journal Title, Volume, Page: 
Math. Phys. 52, 122108
Year of Publication: 
2011
Link: 
http://jmp.aip.org/resource/1/jmapaq/v52/i12/p122108_s1
Authors: 
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, North Cyprus, Turkey
Current Affiliation: 
Department of Physics, An-Najah National University, Nablus, Palestine
[email protected]
Ramazan Sever
Department of Physics, Middle East Technical University, 06800 Ankara, Turkey
Preferred Abstract (Original): 
A nonpolynomial one-dimensional quantum potential in the form of an isotonic oscillator (harmonic oscillator with a centripetal barrier) is studied. We provide the nonrelativistic bound state energy spectrum En and the wave functions ψn(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.