Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions
D. Agboola
Department of Mathematics, School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia
Received: July 3, 2010; In final form: May 27, 2011
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The exact solutions of the N-dimensional Schrödinger equation with the Mie-type potentials are obtained. The energy levels are worked out and the corresponding wave functions are obtained in terms of the Laguerre polynomial. Some energy levels of some diatomic molecules are given using the modified Kratzer-type potential. 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 constructed for the Mie-type potentials in N-dimensions and the matrix elements of some operators r and r·d/dr are analytically obtained from the ladder operators. The general results reduce to the 3-dimensional case when N = 3.
DOI: 10.12693/APhysPolA.120.371
PACS numbers: 03.65.-w, 03.65.Fd, 03.65.Ge