On position and momentum operators in theq-oscillator

Autor:	A U Klimyk
Rok vydání:	2005
Předmět:	Mathematical analysis Physical system General Physics and Astronomy Creation and annihilation operators Statistical and Nonlinear Physics Eigenfunction Operator theory Spectral line Momentum Position (vector) Order (group theory) Mathematical Physics Mathematical physics Mathematics
Zdroj:	Journal of Physics A: Mathematical and General. 38:4447-4458
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/38/20/011
Popis:	The position and momentum operators of the q-oscillator (with the main relation aa+ − qa+a = 1) are symmetric but not self-adjoint if q > 1. They have one-parameter family of self-adjoint extensions. These extensions are given explicitly. Their spectra and eigenfunctions are derived. Spectra of different extensions do not intersect. The results show that the creation and annihilation operators a+ and a of the q-oscillator at q > 1 cannot determine a physical system without further more precise definition. In order to determine a physical system we have to choose appropriate self-adjoint extensions of the position and momentum operators.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5c56bdae0d579c91d4967c44fc907c3f https://doi.org/10.1088/0305-4470/38/20/011 Zobrazit plný text záznamu