Harmonic Oscillator SUSY Partners and Evolution Loops
David J. Fern\'andez C
TL;DR
This paper explores how supersymmetric quantum mechanics applied to the harmonic oscillator can generate partner Hamiltonians that produce evolution loops and geometric phases, enriching the understanding of quantum dynamics.
Contribution
It demonstrates that SUSY partner Hamiltonians of the harmonic oscillator can generate evolution loops and analyzes their geometric phases.
Findings
SUSY partner Hamiltonians produce evolution loops
Geometric phases are characterized in these systems
New insights into quantum evolution dynamics
Abstract
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.
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