6 research outputs found
Deformed su(1,1) Algebra as a Model for Quantum Oscillators
The Lie algebra can be deformed by a reflection
operator, in such a way that the positive discrete series representations of
can be extended to representations of this deformed
algebra . Just as the positive discrete series
representations of can be used to model a quantum
oscillator with Meixner-Pollaczek polynomials as wave functions, the
corresponding representations of can be utilized to
construct models of a quantum oscillator. In this case, the wave functions are
expressed in terms of continuous dual Hahn polynomials. We study some
properties of these wave functions, and illustrate some features in plots. We
also discuss some interesting limits and special cases of the obtained
oscillator models
On the direct limit from pseudo-Jacobi polynomials to Hermite polynomials
In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon 2F1-type hypergeometric transformation formulas, which are applicable to even and odd polynomials separately. This limit opens the way to studying new exactly solvable harmonic oscillator models in quantum mechanics in terms of pseudo-Jacobi polynomials
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