English

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.

Keywords

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

R2 v1 2026-06-21T16:23:27.976Z