Quantum Hamilton-Jacobi Quantization and Shape Invariance
Quantum Physics
2023-07-12 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2212.01871,
title = {Quantum Hamilton-Jacobi Quantization and Shape Invariance},
author = {Rathi Dasgupta and Asim Gangopadhyaya},
journal= {arXiv preprint arXiv:2212.01871},
year = {2023}
}