Higher Order SUSY in Quantum Mechanics and Integrability of Twodimensional 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 2dim 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 2nd order in derivatives. The particular solutions are obtained also for potentials accepting symmetry operators of 4th 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 4th order in momenta. The general SUSYinspired algorithm to construct classical systems with additional integrals of motion is outlined.
 Publication:

arXiv eprints
 Pub Date:
 May 1996
 DOI:
 10.48550/arXiv.solvint/9605007
 arXiv:
 arXiv:solvint/9605007
 Bibcode:
 1996solv.int..5007A
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 High Energy Physics  Theory
 EPrint:
 11 pages, LaTeX