Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians

Details Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians

1996-05-27

arxiv.org/abs/solv-int/9605007v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX

Scientific paper

The new method based on the SUSY algebra with supercharges of higher order in derivatives is proposed to search for dynamical symmetry operators in 2-dim quantum and classical systems. These symmetry operators arise when closing the SUSY algebra for a wide set of potentials. In some cases they are of 2-nd order in derivatives. The particular solutions are obtained also for potentials accepting symmetry operators of 4-th order. The investigation of quasiclassical limit of the SUSY algebra yields new classical integrals of motion for a certain type of systems which are polynomials of 4-th order in momenta. The general SUSY-inspired algorithm to construct classical systems with additional integrals of motion is outlined.

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