Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

• Authors: D. Agboola
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

03.65.-w; 03.65.Fd; 03.65.Ge

Discipline

• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 03.65.Ge: Solutions of wave equations: bound states

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2011
• Volume: 120
• Issue: 3
• Pages: 371-377

Dates

published

2011-09

received

2010-07-03

(unknown)

2011-05-27

Contributors

author

D. Agboola

• Department of Mathematics, School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia

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Identifiers

DOI

10.12693/APhysPolA.120.371