General solutions of the pseudo-diffusion equation of squeezed states

J. Daboul, M. A. Marchiolli, S. S. Mizrahi

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Abstract

We show that the projection operator mod pq;yei phi)(ye i phi;pq mod , where mod pq;yei phi) is a squeezed state, obeys a partial differential equation in which the squeeze parameter y plays the role of time. It follows that related functions, such as the probability distribution functions and the Wigner function are solutions of this equation. This equation will be called a pseudodiffusion equation, because it resembles a diffusion equation in Minkowski space. We give general solutions of the pseudo-diffusion equation, first by the method of separation of variables and then by the Fourier transform method, and discuss the limitations of the latter method. The Fourier method is used to introduce squeezing into the number states, the thermal light and the Wigner function.

Original languageEnglish
Article number019
Pages (from-to)4623-4637
Number of pages15
JournalJournal of Physics A: Mathematical and General
Volume28
Issue number16
DOIs
StatePublished - 1 Dec 1995

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