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arXiv · 1010.0620

Generalized quantum isotonic nonlinear oscillator in d dimensions

Richard L. Hall·Nasser Saad·Ozlem Yesiltas
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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.

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Richard L. Hall, Nasser Saad, Ozlem Yesiltas. 2010-10-04. Generalized quantum isotonic nonlinear oscillator in d dimensions. https://doi.org/10.1088/1751-8113/43/46/465304

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