English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The phase space representation for a q-deformed model of the quantum harmonicoscillator is constructed. We have found explicit expressions for both theWigner and Husimi distribution functions for the stationary states of the$q$-oscillator model under consideration. The Wigner function is expressed as abasic hypergeometric series, related to the Al-Salam-Chihara polynomials. It isshown that, in the limit case $h \to 0$ ($q \to 1$), both the Wigner and Husimidistribution functions reduce correctly to their well-known non-relativisticanalogues. Surprisingly, examination of both distribution functions in theq-deformed model shows that, when $q \ll 1$, their behaviour in the phase spaceis similar to the ground state of the ordinary quantum oscillator, but with adisplacement towards negative values of the momentum. We have also computed themean values of the position and momentum using the Wigner function. Unlike theordinary case, the mean value of the momentum is not zero and it depends on $q$and $n$. The ground-state like behaviour of the distribution functions forexcited states in the q-deformed model opens quite new perspectives for furtherexperimental measurements of quantum systems in the phase space.Comment: 16 pages, 24 EPS figures, uses IOP style LaTeX, some misprints are  correctd and journal-reference is adde

The Wigner function of aq-deformed harmonic oscillator model