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.

arXiv:1205.6239Symmetry Integrability and Geometry Methods and ApplicationsJul 11, 20123 citations

Supersymmetric quantum mechanics and solvable potentials

Aytül Bal

Jan 1, 20150 citations

arXiv:quant-ph/0602218 · Physics Letters A

Exact propagators for complex SUSY partners of real potentials

B. F. Samsonov, Andrey M. Pupasov-Maksimov

Published Apr 1, 2006• 9 citations

arXiv HTML PDF

DOI: 10.1016/j.physleta.2006.03.053

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^{85}

. Conservative SUSY transformations of the first and the second order have been studied in the case of multichannel Schrodinger equation with equal thresholds. Transformations which introduce non-trivial coupling between scattering channels have been founded. The first order SUSY transformation which preserves

S

-matrix eigen-phase shifts and modifies mixing parameter has been founded in the case of two channel scattering with partial waves of different parities. In the case of coinciding parities we have found the second order SUSY transformation which preserves

S

-matrix eigen-phase shifts and modifies mixing parameter. Phenomenological two channel

^3S_1-^3D_1

neutron-proton potential has been obtained by using single channel, phase equivalent and coupling SUSY transformations applied to zero potential.