197 research outputs found
Parasupersymmetric Quantum Mechanics with Generalized Deformed Parafermions
A superposition of bosons and generalized deformed parafermions corresponding
to an arbitrary paraquantization order is considered to provide
deformations of parasupersymmetric quantum mechanics. New families of
parasupersymmetric Hamiltonians are constructed in connection with two examples
of su(2) nonlinear deformations such as introduced by Polychronakos and Ro\v
cek.Comment: 9 pages, LaTeX, no figures, to be published in Helv. Phys. Act
On oscillatorlike Hamiltonians and squeezing
Generalizing a recent proposal leading to one-parameter families of
Hamiltonians and to new sets of squeezed states, we construct larger classes of
physically admissible Hamiltonians permitting new developments in squeezing.
Coherence is also discussed.Comment: 15 pages, Late
A General Approach of Quasi-Exactly Solvable Schroedinger Equations with Three Known Eigenstates
We propose a general method for constructing quasi-exactly solvable
potentials with three analytic eigenstates. These potentials can be real or
complex functions but the spectrum is real. A comparison with other methods is
also performed
A General Approach of Quasi-Exactly Solvable Schroedinger Equations
We construct a general algorithm generating the analytic eigenfunctions as
well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians.
Both exact and quasi-exact Hamiltonians enter our formalism but we focus on
quasi-exact interactions for which no such general approach has been considered
before. In particular we concentrate on a generalized sextic oscillator but
also on the Lame and the screened Coulomb potentials.Comment: 23 pages, no figur
Pseudospin, Spin, and Coulomb Dirac-Symmetries: Doublet Structure and Supersymmetric Patterns
Relativistic symmetries of the Dirac Hamiltonian with a mixture of
spherically symmetric Lorentz scalar and vector potentials, are examined from
the point of view of supersymmetric quantum mechanics. The cases considered
include the Coulomb, pseudospin and spin limits relevant, respectively, to
atoms, nuclei and hadrons.Comment: 8 pages, 1 figure, Proc. Int. Workshop on "Blueprints for the
Nucleus: From First Principles to Collective Motion", May 17-23, 2004, Feza
Gursey Institute, Istanbul, Turke
On realizations of nonlinear Lie algebras by differential operators
We study realizations of polynomial deformations of the sl(2,R)- Lie algebra
in terms of differential operators strongly related to bosonic operators. We
also distinguish their finite- and infinite-dimensional representations. The
linear, quadratic and cubic cases are explicitly visited but the method works
for arbitrary degrees in the polynomial functions. Multi-boson Hamiltonians are
studied in the context of these ``nonlinear'' Lie algebras and some examples
dealing with quantum optics are pointed out.Comment: 21 pages, Latex; New examples added in Sect.
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