2009/02/18 by J. M. Fellows, Robert A. Smith, Fellows, Jonathan M +1
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.0902.3105
openalex publication_date 2009/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper Cariñena 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 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 be exactly solved in a similar manner.