The Wigner equation in the presence of electromagnetic potentials

An analysis of the possible formulations of the Wigner equation under a general gauge for the electric field is presented with an emphasis on the computational aspects of the problem. The numerical peculiarities of those formulations enable alternative computational strategies based on existing numerical methods applied in the Wigner formalism, such as finite difference or stochastic particle methods. The phase space formulation of the problem along with certain relations to classical mechanics offers an insight about the role of the gauge transforms in quantum mechanics.