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Journal of Physics Conference Series

Arbitrarylstate solutions of the Schrödinger equation with the Deng-Fan molecular potential

S-H Dong, X-Y Gu

Published Feb 1, 2008• 76 citations
Publisher

Abstract

The bound state solutions of the Schrödinger equation with the rotating Deng-Fan molecular potential are presented approximately. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived. To show the accuracy of our results, the eigenvalues calculated numerically for arbitrary quantum numbers n and l with two different values of the parameter r e are in good agreement with those obtained by the MATHEMATICA package for short potential range.

DOI
10.1088/1742-6596/96/1/012109

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The bound state solutions of the Schrödinger equation with the rotating Deng-Fan molecular potential are presented approximately. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived. To show the accuracy of our results, the eigenvalues calculated numerically for arbitrary quantum numbers n and l with two different values of the parameter r e are in good agreement with those obtained by the MATHEMATICA package for short potential range.
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In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.
The approximate analytical solutions of the radial Schrӧdinger equation have been obtained with a newly proposed potential called Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential and generalized Morse or Deng-Fan potential. The Hellmann-generalized Morse potential actually comprises of three different potentials which includes Yukawa potential, Coulomb potential and Deng-Fan potential. The aim of combining these potentials is to have a wide application. The energy eigenvalue and the corresponding wave function are calculated in a closed and compact form using the parametric Nikiforov-Uvarov method. The energy equation for some potentials such as Deng-Fan, Rosen Morse, Morse, Hellmann, Yukawa and Coulomb potentials have also been obtained by varying some potential parameters. Some numerical results have been computed. We have plotted the behavior of the energy eigenvalues with different potential parameters and also reported on the numerical result. Finally, we computed the variance and information energy for the Hellmann-generalized Morse potential.
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.