A q-deformation of the Gauss distribution (2000)
| Venue: | J. Math. Phys |
| Citations: | 13 - 2 self |
BibTeX
@ARTICLE{Leeuwen00aq-deformation,
author = {Hans Van Leeuwen and Hans Maassen},
title = {A q-deformation of the Gauss distribution},
journal = {J. Math. Phys},
year = {2000},
volume = {36},
pages = {4743--4756}
}
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Abstract
The q-deformed commutation relation aa # - qa # a = 11 for the harmonic oscillator is considered with q # [-1, 1]. An explicit representation generalizing the Bargmann representation of analytic functions on the complex plane is constructed. In this representation the distribution of a + a # in the vacuum state is explicitly calculated. This distribution is to be regarded as the natural q- deformation of the Gaussian. 1995 PACS numbers: 02.50.Cw, 05.40.+j, 03.65.Db, 42.50.Lc 1991 MSC numbers: 81S25, 33D90, 81Q10 1 1
