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Physical Science International Journal

Arbitrary l-state Solution of the Schrödinger Equation for q-deformed Attractive Radial Plus Coulomb-like Molecular Potential within the Framework of NU-Method

B. I. Ita, Hitler Louis, Innocent Joseph, Ikeuba I. Alexander, Pigweh Isa Amos, Thomas O. Magu

Published Dec 22, 2017• 1 citation
Publisher

Abstract

The Schrödinger equation in one dimension for the q-deformed attractive radial plus coulomb-like molecular potential (ARCMP) is solved approximately to obtain bound states eigen solutions using the parametric Nikiforov-Uvarov (NU) method. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials. Interestingly, the resulting eigen energy equations can be used to study the spectroscopy of some selected diatomic atoms and molecules.

DOI
10.9734/psij/2017/38034

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The Schrödinger equation in one dimension for the q-deformed attractive radial plus coulomb-like molecular potential (ARCMP) is solved approximately to obtain bound states eigen solutions using the parametric Nikiforov-Uvarov (NU) method. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials. Interestingly, the resulting eigen energy equations can be used to study the spectroscopy of some selected diatomic atoms and molecules.
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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.
We study the nonrelativistic Schrödinger equation for q-deformed Hulthen plus modified inversely quadratic Yukawa potential using the generalized parametric form of NIkiforov-Uvarov method. The energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric function are obtained. We have also discussed four (4) special cases of this potential, i.e. Woods-Saxon, Hulthen, Morse and inversely quadratic potentials. Keywords: Nonrelativistic Schrödinger equation, q-deformed Hulthen potential, modified inversely quadratic Yukawa potential, parametric Nikiforov-Uvarov method.
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method.We also obtained the energy eigen value and its associated total wave function .This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential.Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter.The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant).The graph in figure (1) shows the different energy levels for a particular quantum number.
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_{n}^{(\mu,\nu)}(x), where \mu>-1, \nu>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_{2} and Ar_{2} molecules are also calculated and compared with the previous models and experiments.