7 research outputs found
Coherent states for Hamiltonians generated by supersymmetry
Coherent states are derived for one-dimensional systems generated by
supersymmetry from an initial Hamiltonian with a purely discrete spectrum for
which the levels depend analytically on their subindex. It is shown that the
algebra of the initial system is inherited by its SUSY partners in the subspace
associated to the isospectral part or the spectrum. The technique is applied to
the harmonic oscillator, infinite well and trigonometric Poeschl-Teller
potentials.Comment: LaTeX file, 26 pages, 3 eps figure
Invariant vector fields and the prolongation method for supersymmetric quantum systems
The kinematical and dynamical symmetries of equations describing the time
evolution of quantum systems like the supersymmetric harmonic oscillator in one
space dimension and the interaction of a non-relativistic spin one-half
particle in a constant magnetic field are reviewed from the point of view of
the vector field prolongation method. Generators of supersymmetries are then
introduced so that we get Lie superalgebras of symmetries and supersymmetries.
This approach does not require the introduction of Grassmann valued
differential equations but a specific matrix realization and the concept of
dynamical symmetry. The Jaynes-Cummings model and supersymmetric
generalizations are then studied. We show how it is closely related to the
preceding models. Lie algebras of symmetries and supersymmetries are also
obtained.Comment: 37 pages, 7 table
Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
Nonlinear SUSY approach to preparation of quantum systems with pre-planned
spectral properties is reviewed. Possible multidimensional extensions of
Nonlinear SUSY are described. The full classification of ladder-reducible and
irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence
of hidden symmetries and spectrum generating algebras is elucidated in the
context of Nonlinear SUSY in one- and two-dimensional QM.Comment: 75 pages, Minor corrections, Version published in Journal of Physics