Fellows, Jonathan M.; Smith, Robert A. Factorization solution of a family of quantum nonlinear oscillators. (English) Zbl 1177.81034 J. Phys. A, Math. Theor. 42, No. 33, Article ID 335303, 13 p. (2009). Summary: In a recent paper, J. F. Cariñena, A. M. Perelomov, M. F. Rañada and M. Santander [J. Phys. A, Math. Theor. 41, No. 8, Article ID 085301 (2008; Zbl 1138.81380)] analyzed a non-polynomial one-dimensional quantum potential representing an oscillator which they argued was intermediate between the harmonic and isotonic oscillators. In particular, they proved that it is Schrödinger soluble, and explicitly obtained the wavefunctions and energies of the bound states. In this paper, we show that these results can be obtained much more simply by noting that this potential is a supersymmetric partner potential of the harmonic oscillator. We then use this observation to generate an infinite set of potentials which can exactly be solved in a similar manner. Cited in 1 ReviewCited in 28 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations) Citations:Zbl 1138.81380 PDFBibTeX XMLCite \textit{J. M. Fellows} and \textit{R. A. Smith}, J. Phys. A, Math. Theor. 42, No. 33, Article ID 335303, 13 p. (2009; Zbl 1177.81034) Full Text: DOI arXiv