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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
Supersymmetric operators
Being chosen as a differential operator of a special form, metric
operator becomes unitary equivalent to a one-dimensional Hermitian Hamiltonian
with a natural supersymmetric structure. We show that fixing the superpartner
of this Hamiltonian permits to determine both the metric operator and
corresponding non-Hermitian Hamiltonian. Moreover, under an additional
restriction on the non-Hermitian Hamiltonian, it becomes a superpartner of
another Hermitian Hamiltonian.Comment: 15 page
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