Quantum Hamilton-Jacobi Quantization and Shape Invariance

TL;DR

This paper demonstrates that additive shape invariance and unbroken supersymmetry are sufficient for solving quantum systems using the quantum Hamilton-Jacobi method, unifying concepts in quantum mechanics.

Contribution

It proves that shape invariance and supersymmetry guarantee solvability within the quantum Hamilton-Jacobi framework, extending previous methods.

Findings

Shape invariance ensures solvability in the quantum Hamilton-Jacobi scheme.

Unbroken supersymmetry is a sufficient condition for quantum system solvability.

The approach unifies different quantum solvability criteria.

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.