Parasupersymmetric Quantum Mechanics with Generalized Deformed Parafermions

A superposition of bosons and generalized deformed parafermions corresponding to an arbitrary paraquantization order $p$ 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.