Operators of the $q$-oscillator
| dc.creator | Szafraniec, F. H. | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T08:43:58Z | |
| dc.date.available | 2026-07-07T08:43:58Z | |
| dc.description | We scrutinize the possibility of extending the result of \cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our {\it leitmotif} is {\it subnormality}. The deformation parameter $q$ is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator $C$, has two remarkable properties: it separates in the commutation relation the annihilation and creation operators from the deformation as well as it $q$-commutes with those two. This is why introducing the operator $C$ seems to be far-reaching. | |
| dc.description | 14 pp | |
| dc.identifier | https://arxiv.org/abs/0711.3073 | |
| dc.identifier | http://arxiv.org/abs/0711.3073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142497 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47B20, 81S05 | |
| dc.title | Operators of the $q$-oscillator | |
| dc.type | text |