Quantum dynamics and Wigner representation of quantum mechanics

Abstract

Abstract A new method for solving the Wigner-Liouville equation allowing a treatment of quantum dynamics has been developed. The method combines two widely known approaches: molecular dynamics and Monte Carlo. Numerical results have been obtained for one-, two- and three-dimensional potential wells of realistic type. The quantum dynamics method was tested by a comparison of the numerical results with analytical estimates for such values as the average position x¯(t), average momentum p¯(t), energy Ē(t), position and momentum dispersions, and Heisenberg inequality.