Operators of the q-oscillator

Franciszek Hugon Szafraniec. "Operators of the q-oscillator." Banach Center Publications 78.1 (2007): 293-307. <http://eudml.org/doc/282277>.

@article{FranciszekHugonSzafraniec2007,
abstract = {We scrutinize the possibility of extending the result of [19] 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 leitmotif is 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 may have far-reaching consequences.},
author = {Franciszek Hugon Szafraniec},
journal = {Banach Center Publications},
keywords = {unbounded subnormal operator; -oscillator},
language = {eng},
number = {1},
pages = {293-307},
title = {Operators of the q-oscillator},
url = {http://eudml.org/doc/282277},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Franciszek Hugon Szafraniec
TI - Operators of the q-oscillator
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 293
EP - 307
AB - We scrutinize the possibility of extending the result of [19] 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 leitmotif is 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 may have far-reaching consequences.
LA - eng
KW - unbounded subnormal operator; -oscillator
UR - http://eudml.org/doc/282277
ER -