Harmonic Oscillator SUSY Partners and Evolution Loops

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.

References in corpus (3)

• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Fractional supersymmetry and hierarchy of shape invariant potentials
• Non-hermitian Hamiltonians and Painlevé IV equation with real parameters