Factorization solution of a family of quantum nonlinear oscillators

Jonathan Fellows, Robert Smith

Research output: Contribution to journalArticle

52 Citations (Scopus)


In a recent paper, Carinena J F, Perelomov A M, Ranada M F and Santander M (2008 J. Phys. A: Math. Gen. 41 085301) 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 Schrodinger 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.
Original languageEnglish
Pages (from-to)335303
Number of pages1
JournalJournal of Physics A: Mathematical and Theoretical
Issue number33
Publication statusPublished - 1 Aug 2009


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