Variable Mass Quantum Harmonic Oscillator; Exact Solvability and Isospectral Potentials

By imposing a particular constraint of solvability on the Liouville normal form of the BenDaniel-Duke type variable mass Schr¨odinger equation, we have derived a class of solvable potentials and harmonic oscillator type solutions for the system. The method has been shown to be applicable in finding isospectral potentials for an infinite possibility of position-dependent mass distributions as well as in determining the effective mass profile for a given effective interaction.