Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

TL;DR

This paper explores how Wigner distribution functions can represent time-dependent canonical transformations in quantum mechanics, focusing on incorporating evolving uncertainties into phase space formalism.

Contribution

It introduces a method to include the time dependence of uncertainties in the Wigner function representation of quantum canonical transformations.

Findings

Incorporates time-dependent uncertainties into phase space formalism.

Provides a framework for representing time-dependent quantum transformations.

Enhances understanding of quantum dynamics in phase space.

Abstract

For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.