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arXiv:0812.3780

Complete Analytic Solutions of the Mie-type Potentials in N-Dimensions

D. Agboola

Published Dec 19, 2008• 2 citations
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Abstract

The exact solutions of the N-dimensional Schrodinger equation with the Mie-type potentials are obtained using the conventional Nikiforov-Uvarov method.The expectation values r^{-1} and r^{-2}$ and the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem.The ladder operators are also construct for the Mie-type potentials in N-dimensions and the matrix elements of some operators $r$ and r\frac{d}{dr} are analytically obtained from the ladder operators.And the general results reduce to the 3-dimensional case when N=3.

DOI
10.48550/arxiv.0812.3780

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The exact solutions of the N-dimensional Schrodinger equation with the Mie-type potentials are obtained using the conventional Nikiforov-Uvarov method.The expectation values r^{-1} and r^{-2}andthevirialtheoremarealsoobtainedinN−dimensionsusingtheHellmann−Feynmantheorem.TheladderoperatorsarealsoconstructfortheMie−typepotentialsinN−dimensionsandthematrixelementsofsomeoperatorsand the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem.The ladder operators are also construct for the Mie-type potentials in N-dimensions and the matrix elements of some operatorsandthevirialtheoremarealsoobtainedinN−dimensionsusingtheHellmann−Feynmantheorem.TheladderoperatorsarealsoconstructfortheMie−typepotentialsinN−dimensionsandthematrixelementsofsomeoperatorsr$ and r\frac{d}{dr} are analytically obtained from the ladder operators.And the general results reduce to the 3-dimensional case when N=3.
The general solutions of the Schrödinger equation for a non-central potential are obtained by using the Nikiforov–Uvarov method. The Schrödinger equation with general non-central potential is separated into radial and angular parts, and energy eigenvalues and eigenfunctions are derived analytically. By making special selections, the non-central potential is reduced to Coulomb and Hartmann ring-shaped potentials, and the obtained results are compared with the solutions of Coulomb and Hartmann potentials given in the literature.
The general solutions of Schrodinger equation for non central potential are obtained by using Nikiforov Uvarov method. The Schrodinger equation with general non central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions for these potentials are derived analytically. Non central potential is reduced to Coulomb and Hartmann potential by making special selections, and the obtained solutions are compared with the solutions of Coulomb and Hartmann ring shaped potentials given in literature.