Operators of the q-oscillator

• Autorzy: Franciszek Hugon Szafraniec
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 81S05: Canonical quantization, commutation relations and statistics
• 47B20: Subnormal operators, hyponormal operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 293-307

Daty

wydano

2007

Twórcy

autor

Franciszek Hugon Szafraniec

• Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/bc78-0-22