Exactly complete solutions of the pseudoharmonic potential in N-dimensions

Oyewumi, K. J., Akinpelu, F. O. and Agboola, A. D. (2008) Exactly complete solutions of the pseudoharmonic potential in N-dimensions. International Journal of Theoretical Physics, 47 4: 1039-1057. doi:10.1007/s10773-007-9532-x


Author Oyewumi, K. J.
Akinpelu, F. O.
Agboola, A. D.
Title Exactly complete solutions of the pseudoharmonic potential in N-dimensions
Journal name International Journal of Theoretical Physics   Check publisher's open access policy
ISSN 0020-7748
Publication date 2008
Sub-type Article (original research)
DOI 10.1007/s10773-007-9532-x
Volume 47
Issue 4
Start page 1039
End page 1057
Total pages 19
Language eng
Subject 3100 Physics and Astronomy
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〉, 〈r 2〉, 〈T〉, 〈V〉, 〈H〉, 〈p 2〉 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.
Keyword Exact solutions
Expectation values
Hellmann-Feynman theorems
Hyperspherical harmonics
Ladder operators
N-dimensions
Pseudoharmonic oscillator potential
Schrödinger equation
SU(1, 1)
Virial theorems
Wavefunction ansatz
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Fri, 18 Mar 2016, 22:01:40 EST by Davids Agboola