Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 1996
- DOI:
- 10.48550/arXiv.solv-int/9605007
- arXiv:
- arXiv:solv-int/9605007
- Bibcode:
- 1996solv.int..5007A
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory
- E-Print:
- 11 pages, LaTeX