6,956 research outputs found
Time-dependent parasupersymmetry in quantum mechanics
Parasupersymmetry of the one dimensional time-dependent Schr\"odinger
equation is established. It is intimately connected with a chain of the
time-dependent Darboux transformations. As an example a parasupersymmetric
model of nonrelativistic free particle with threefold degenerate discrete
spectrum of an integral of motion is constructed.Comment: 11pages, latex, amsfonts, no figure
Irreducible second order SUSY transformations between real and complex potentials
Second order SUSY transformations between real and complex potentials for
three important from physical point of view Sturm-Liouville problems, namely,
problems with the Dirichlet boundary conditions for a finite interval, for a
half axis and for the whole real line are analyzed. For every problem
conditions on transformation functions are formulated when transformations are
irreducible, i.e. when either the intermediate Hamiltonian is not well defined
in the same Hilbert space as the initial and final Hamiltonians or its
eigenfunctions cannot be obtained by applying transformation operator either on
eigenfunctions of the initial Hamiltonian or on these of the final Hamiltonian.
Obtained results are illustrated by numerous simple examples.Comment: Thanks to M.V. Ioffee Ref. [13] is corrected in the second versio
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