Hans van Leeuwen, Hans Maassen
A q-deformation of the Gauss distribution
(46K, LaTeX2e)
ABSTRACT. The q-deformed commutation relation a a* - q a* a = 1 for the harmonic
oscillator is considered with q in [-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.