Generalized quantum isotonic nonlinear oscillator in d dimensions

Details Generalized quantum isotonic nonlinear oscillator in d dimensions Generalized quantum isotonic nonlinear oscillator in d dimensions

2010-10-04

arxiv.org/abs/1010.0620v1

J.Phys.A43:465304,2010

Physics

Mathematical Physics

8 pages, no figures

Scientific paper

10.1088/1751-8113/43/46/465304

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.

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