Bohmian and quantum phase space distribution expansions and approximations

Abstract

Abstract Dias and Patra derived an expansion of the Wigner distribution and related it to the de Broglie–Bohm model. We show that the coefficients of the expansion are related to the conditional central moments and cumulants of the Wigner distribution. The even order cumulants depend only on the amplitude of the wave function and the odd order cumulants depend only on the phase. In addition, we give a different expansion of the Wigner distribution from which their expansion can be derived as a special case. Our expansion allows for different approximations for higher order terms. We also give expansions for the momentum representation. We show how the results are applicable to pulse propagation in a dispersive medium.