Wigner equations of motion for classical systems

Lorenzo Galleani; Leon Cohen

doi:10.1117/12.406530

13 November 2000 Wigner equations of motion for classical systems

Lorenzo Galleani, Leon Cohen

Proceedings Volume 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X; (2000) https://doi.org/10.1117/12.406530
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We present a general procedure for obtaining equations of motion for the Wigner distribution of functions that are governed by ordinary and partial differential equations. For the case of fields we show that in general one must consider Wigner distribution of the four variables, position, momentum, time and frequency. We also show that in general one cannot write an equation of motion for position and momentum however it can be done in some cases, the Schrodinger equation being one such case. Our method leads to an equation of motion for the Schrodinger equation with time dependent potentials in contrast to the result obtained by Wigner and Moyal which was for time independent potentials.

Citation Download Citation

Lorenzo Galleani and Leon Cohen "Wigner equations of motion for classical systems", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); https://doi.org/10.1117/12.406530

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