Nonlinear Schrödinger and gross - Pitaevskii equations in the Bohmian or Quantum Fluid Dynamics (QFD) representation

Abstract

The Quantum Fluid Dynamics (QFD) representation has its foundations in the works of Madelung (1929), De Broglie (1930 - 1950) and Bohm (1950 - 1970). It is an interpretation of quantum mechanics with the goal to find classically identifiable dynamical variables at the sub-particle level. The approach leads to two conservation laws, one for "mass" and one for "momentum", similar to those in hydrodynamics for a compressible fluid with a particular constitutive law. The QFD equations are a set of nonlinear partial differential equations. This paper extends the QFD formalism of quantum mechanics to the Nonlinear Schrödinger and the Gross-Pitaevskii equation.