24 research outputs found
On the Wigner function of the relativistic finite-difference oscillator in an external field
The phase-space representation for a relativistic linear oscillator in a
homogeneous external field expressed through the finite-difference equation is
constructed. Explicit expressions of the relativistic oscillator Wigner
quasi-distribution function for the stationary states as well as of states of
thermodynamical equilibrium are obtained and their correct limits are shown.Comment: 12 pages, 6 figures, IOP styled LaTeX, to be published in Journal of
Physics
The Relativistic Linear Singular Oscillator
Exactly-solvable model of the linear singular oscillator in the relativistic
configurational space is considered. We have found wavefunctions and energy
spectrum for the model under study. It is shown that they have correct
non-relativistic limits.Comment: 14 pages, 12 figures in eps format, IOP style LaTeX file (revised
taking into account referees suggestions
Group Approach to the Quantization of the P\"oschl-Teller dynamics
The quantum dynamics of a particle in the Modified P\"oschl-Teller potential
is derived from the group by applying a Group Approach to
Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder
operators is found in the enveloping algebra of this basic symmetry group. The
present algorithm provides a physical realization of the non-unitary,
finite-dimensional, irreducible representations of the group. The
non-unitarity manifests itself in that only half of the states are
normalizable, in contrast with the representations of SU(2) where all the
states are physical.Comment: 17 pages, LaTe