Comparison of classical and quantal evolution of phase space distribution functions

Abstract

Classical and quantum dynamics are compared in phase space and at the hydrodynamic level for one dimensional motion. An internal potential is defined as a common object to both classical statistical mechanics and to quantum mechanics. It reduces to the quantum potential in the quantum pure state case, but its presence and roll in determining the dynamics of the system is equally valid for classical flows and quantum mixed states. A numerical example is provided to illustrate the extent of the similarity between both mechanics in a scattering process where classical and quantum transmittances are alike.