Tokiniaina Ranaivoson, Raoelina Andriambololona, Rakotoson Hanitriarivo, Roland Raboanary
A study on a method to establish phase space representation of quantum theories is presented. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials, Fourier analysis and linear operators theory. Phase space representation of quantum state and wave functions in phase space are introduced using properties of a set of functions that we call harmonic Gaussian functions. Then, new operators that we designate dispersion operators are defined as the operators which admit as eigenstates the states associated to the phase space representation. Generalization of the approach for multidimensional case is shown. Examples of application are given too.
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http://arxiv.org/abs/1304.1034
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