TY - JOUR

T1 - General solutions of the pseudo-diffusion equation of squeezed states

AU - Daboul, J.

AU - Marchiolli, M. A.

AU - Mizrahi, S. S.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21844496523&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/28/16/019

DO - 10.1088/0305-4470/28/16/019

M3 - Article

AN - SCOPUS:21844496523

VL - 28

SP - 4623

EP - 4637

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 16

M1 - 019

ER -