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Communications in Theoretical Physics

Solutions of the Schrödinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

Benedict I. Ita, Alexander Immaanyikwa Ikeuba, A. N. Ikot

Published Feb 1, 2014• 14 citations
Publisher

Abstract

The solutions of the Schrödinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov—Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.

DOI
10.1088/0253-6102/61/2/01

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The solutions of the Schrödinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov—Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.
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Abstract The energy spectrum of the velocity-dependent potentials with respect to the harmonic oscillator potential and Coulomb potential are obtained for any n and l quantum states using the Nikiforov–Uvarov method for different cases of velocity-dependent terms. The effects of isotropic velocity-dependent potentials on the bound state energy eigenvalues are examined in analytic form when the form factor is considered as ξ ( r ) = γ r and ξ ( r ) = γ r 2 . As an application to a physical system, we evaluated the vibrational partition function and other thermodynamic properties for the isotropic velocity-dependent potential harmonic oscillator.
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