Generalized quantum isotonic nonlinear oscillator in d dimensions
Mathematical Physics
2011-03-28 v1 math.MP
Quantum Physics
Abstract
We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r)={B^2}/{r^{2}}+\omega^{2} r^{2}+2g{(r^{2}-a^{2})}/{(r^{2}+a^{2})^{2}}, B\geq 0. We show that the eigenequation for this potential is exactly solvable provided g=2 and (\omega a^2)^2 = B^2 +(\ell +(d-2)/2)^2. Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.
Cite
@article{arxiv.1010.0620,
title = {Generalized quantum isotonic nonlinear oscillator in d dimensions},
author = {Richard L. Hall and Nasser Saad and Ozlem Yesiltas},
journal= {arXiv preprint arXiv:1010.0620},
year = {2011}
}
Comments
8 pages, no figures