Quantum Hamilton–Jacobi quantization and shape invariance

Abstract

Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known conventional potentials. Using a recent work in supersymmetric quantum mechanics, we prove that the additive shape invariance of all conventional potentials and unbroken supersymmetry are sufficient conditions for their solvability within the quantum Hamilton-Jacobi formalism.