Exactly solvable systems and the Quantum Hamilton-Jacobi formalism
Constantin Rasinariu, John J. Dykla, Asim Gangopadhyaya, Jeffry V., Mallow
TL;DR
This paper links Quantum Hamilton-Jacobi theory with supersymmetric quantum mechanics, revealing that shape invariance corresponds to fractional linear relations among quantum momentum functions, thus providing a new perspective on integrability.
Contribution
It establishes a connection between Quantum Hamilton-Jacobi formalism and SUSYQM, demonstrating how shape invariance translates into fractional linear relations.
Findings
Shape invariance corresponds to fractional linear relations among quantum momentum functions.
The connection provides a new perspective on integrability in quantum systems.
The formalism offers exact solutions for certain quantum systems.
Abstract
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum momentum functions.
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