GENERAL-SOLUTIONS OF THE PSEUDO-DIFFUSION EQUATION OF SQUEEZED STATES

We show that the projection operator \pq; ye(i phi)][ye(i phi); pq\, w here \pq; ye(i phi)] is a squeezed stare, 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 f unctions and the Wigner function are solutions of this equation. This equation will be called a pseudo-diffusion equation, because it resemb les a diffusion equation in Minkowski space. We give general solutions of the pseudo-diffusion equation, first by the method of separation o f variables and then by the Fourier transform method, and discuss the limitations of the latter method. The Fourier method is used to introd uce squeezing into the number states, the thermal light and the Wigner function.