2 research outputs found
A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
The supersymmetrical approach is used to analyse a class of two-dimensional
quantum systems with periodic potentials. In particular, the method of
SUSY-separation of variables allowed us to find a part of the energy spectra
and the corresponding wave functions (partial solvability) for several models.
These models are not amenable to conventional separation of variables, and they
can be considered as two-dimensional generalizations of Lame, associated Lame,
and trigonometric Razavy potentials. All these models have the symmetry
operators of fourth order in momenta, and one of them (the Lame potential)
obeys the property of self-isospectrality.Comment: 22 pages; some typos corrected; new reference adde
Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
Two known 2-dim SUSY quantum mechanical constructions - the direct
generalization of SUSY with first-order supercharges and Higher order SUSY with
second order supercharges - are combined for a class of 2-dim quantum models,
which {\it are not amenable} to separation of variables. The appropriate
classical limit of quantum systems allows us to construct SUSY-extensions of
original classical scalar Hamiltonians. Special emphasis is placed on the
symmetry properties of the models thus obtained - the explicit expressions of
quantum symmetry operators and of classical integrals of motion are given for
all (scalar and matrix) components of SUSY-extensions. Using Grassmanian
variables, the symmetry operators and classical integrals of motion are written
in a unique form for the whole Superhamiltonian. The links of the approach to
the classical Hamilton-Jacobi method for related "flipped" potentials are
established.Comment: 19 page