779 research outputs found
Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics
A class of integrable 2-dim classical systems with integrals of motion of
fourth order in momenta is obtained from the quantum analogues with the help of
deformed SUSY algebra. With similar technique a new class of potentials
connected with Lax method is found which provides the integrability of
corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim
systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.
Intertwining relations of non-stationary Schr\"odinger operators
General first- and higher-order intertwining relations between non-stationary
one-dimensional Schr\"odinger operators are introduced. For the first-order
case it is shown that the intertwining relations imply some hidden symmetry
which in turn results in a -separation of variables. The Fokker-Planck and
diffusion equation are briefly considered. Second-order intertwining operators
are also discussed within a general approach. However, due to its complicated
structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20
Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics
The iteration procedure of supersymmetric transformations for the
two-dimensional Schroedinger operator is implemented by means of the matrix
form of factorization in terms of matrix 2x2 supercharges. Two different types
of iterations are investigated in detail. The particular case of diagonal
initial Hamiltonian is considered, and the existence of solutions is
demonstrated. Explicit examples illustrate the construction.Comment: 15
Matrix Hamiltonians: SUSY approach to hidden symmetries
A new supersymmetric approach to the analysis of dynamical symmetries for
matrix quantum systems is presented. Contrary to standard one dimensional
quantum mechanics where there is no role for an additional symmetry due to
nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries.
This approach is based on a generalization of the intertwining relations
familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of
first or of second order in derivatives, lead to an algebra which incorporates
an additional block diagonal differential matrix operator (referred to as a
"hidden" symmetry operator) found to commute with the superhamiltonian. We
discuss some physical interpretations of such dynamical systems in terms of
spin 1/2 particle in a magnetic field or in terms of coupled channel problem.
Particular attention is paid to the case of transparent matrix potentials.Comment: 20 pages, LaTe
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