Quantum Hamilton-Jacobi Quantization and Shape Invariance

• URL: http://arxiv.org/abs/2212.01871v3
• Date: Fri, 23 Jun 2023 02:21:12 GMT
• Title: Quantum Hamilton-Jacobi Quantization and Shape Invariance
• Authors: Rathi Dasgupta and Asim Gangopadhyaya
• Abstract summary: Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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