Generalized quantum isotonic nonlinear oscillator in d dimensions

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}}+ω^{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 (ωa^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.

8 pages, no figures

References in corpus (5)

• Supersymmetry and Quantum Mechanics
• A quantum exactly solvable non-linear oscillator related with the isotonic oscillator
• Spiked harmonic oscillators
• The generalized quantum isotonic oscillator
• A basis for variational calculations in d dimensions

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• Finite series representation for the bound states of a spiked isotropic oscillator with inverse-quartic singularity
• Singular Isotonic Oscillator, Supersymmetry and Superintegrability