95-180 Hans van Leeuwen, Hans Maassen

A q-deformation of the Gauss distribution (46K, LaTeX2e) Mar 31, 95

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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.

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