Exact propagators for SUSY partners
Andrey M. Pupasov, Boris F. Samsonov, Uwe Guenther
TL;DR
This paper derives explicit formulas for propagators of supersymmetric partner Hamiltonians, extending solvable quantum models like the harmonic oscillator and free particle to their SUSY counterparts.
Contribution
It provides a general method to obtain propagators for SUSY partner Hamiltonians based on known solutions, applicable to various quantum systems.
Findings
Derived explicit propagator formulas for SUSY partners
Applied results to particle in a box, harmonic oscillator, and free particle
Extended solvable models to SUSY frameworks
Abstract
Pairs of SUSY partner Hamiltonians are studied which are interrelated by usual (linear) or polynomial supersymmetry. Assuming the model of one of the Hamiltonians as exactly solvable with known propagator, expressions for propagators of partner models are derived. The corresponding general results are applied to "a particle in a box", the Harmonic oscillator and a free particle (i.e. to transparent potentials).
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