Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 041, 12 pages      arXiv:1205.6239      https://doi.org/10.3842/SIGMA.2012.041
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Harmonic Oscillator SUSY Partners and Evolution Loops

David J. Fernández
Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F., México

Received May 28, 2012, in final form July 04, 2012; Published online July 11, 2012

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.

Key words: supersymmetric quantum mechanics; quantum harmonic oscillator; polynomial Heisenberg algebra; geometric phase.

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