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Zbl 1177.81034
Fellows, Jonathan M.; Smith, Robert A.
Factorization solution of a family of quantum nonlinear oscillators. (English)
[J] J. Phys. A, Math. Theor. 42, No. 33, Article ID 335303, 13 p. (2009). ISSN 1751-8113; ISSN 1751-8121/e

Summary: In a recent paper, {\it J. F. Cariñena, A. M. Perelomov, M. F. Rañada} and {\it 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.\par 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.

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
35Q55 NLS-like (nonlinear Schroedinger) equations

Citations: Zbl 1138.81380

Cited in: Zbl 1226.81062

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