A q deformation of the Gauss distribution

Abstract

The q deformed commutation relation aa^*−qa^*a=1 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.