arXiv subjects

Jonathan M Fellows

Publications and source records attributed to Jonathan M Fellows.

2 recordsLinked to original sources

arXiv2011

A New Two-Parameter Family of Potentials with a Tunable Ground State

In a previous paper we solved a countably infinite family of one-dimensional Schrödinger equations by showing that they were supersymmetric partner potentials of the standard quantum harmonic oscillator. In this work we extend these results to find the complete set of real partner potentials of the harmonic oscillator, showing that these depend upon two continuous parameters. Their spectra are identical to that of the harmonic oscillator, except that the ground state energy becomes a tunable parameter. We finally use these potentials to analyse the physical problem of Bose-Einstein condensation in an atomic gas trapped in a dimple potential.

quant-ph↗

arXiv2009

Factorization solution of Cariñena's quantum nonlinear oscillator

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.

quant-ph↗