International Journal of Theoretical Physics

, Volume 47, Issue 4, pp 1039–1057

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

  • K. J. Oyewumi
  • F. O. Akinpelu
  • A. D. Agboọla
Article

DOI: 10.1007/s10773-007-9532-x

Cite this article as:
Oyewumi, K.J., Akinpelu, F.O. & Agboọla, A.D. Int J Theor Phys (2008) 47: 1039. doi:10.1007/s10773-007-9532-x

Abstract

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r−2〉, 〈r2〉, 〈T〉, 〈V〉, 〈H〉, 〈p2〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.

Keywords

N-dimensionsPseudoharmonic oscillator potentialSchrödinger equationExact solutionsHyperspherical harmonicsWavefunction ansatzLadder operatorsSU(1, 1)Expectation valuesHellmann–Feynman theoremsVirial theorems

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • K. J. Oyewumi
    • 1
  • F. O. Akinpelu
    • 2
  • A. D. Agboọla
    • 2
  1. 1.Theoretical Physics Section, Department of PhysicsUniversity of IlorinIlorinNigeria
  2. 2.Department of Pure and Applied MathematicsLadoke Akintola University of TechnologyOgbomosoNigeria