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Relativistic and nonrelativistic bound states of the isotonic oscillator by Nikiforov-Uvarov method. (English) Zbl 1273.81071

Summary: 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 \(E_n\) 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.{
©2011 American Institute of Physics}}

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81U15 Exactly and quasi-solvable systems arising in quantum theory
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