A probabilistic approach to some results by Nieto and Truax

Details A probabilistic approach to some results by Nieto and Truax A probabilistic approach to some results by Nieto and Truax

2010-05-12

arxiv.org/abs/1005.2161v2

Physics

Condensed Matter

Statistical Mechanics

2nd version

Scientific paper

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.

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