We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (su-persymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry in...

Witten's non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schrödinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations.

A parametrization of the Hamiltonian of the generalized Witten model of the SUSY QM by a single arbitrary function in d = 1 has been obtained for an arbitrary number of the supersymmetries N . Possible applications of this formalism have been discussed. It has been shown that the N = 1 and 2 conformal SUSY QM is generalized for any N . Submitted to the Physics Letters B.

Standard and non-standard associated Legendre equations and supersymmetric quantum mechanics Abstract. A simple supersymmetric approach recently used by Dutt, Gan-gopadhyaya, and Sukhatme (hep-th/9611087, Am. J. Phys., to appear) for spherical harmonics is generalized to Gegenbauer and Jacobi equations. The coordinate transformation procedure is well known to the authors writing on supersymmetr...

This paper constitutes a review on N = 2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra Wk. It is shown how a general Hamiltonian can be associated with the algebra Wk. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, PöschlTeller system, fractiona...

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulae concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Pöschl-Teller potentials. Some intrinsica...