Factorization solution of Cariñena's quantum nonlinear oscillator

Details Factorization solution of Cariñena's quantum nonlinear oscillator Factorization solution of Cariñena's quantum nonlinear oscillator

2009-02-18

arxiv.org/abs/0902.3105v1

Physics

Quantum Physics

Scientific paper

In a recent paper Cari\~nena et al 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 Schr\"odinger 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 be exactly solved in a similar manner.

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