Quantum hydrodynamics with complex quantities

Abstract

The hydrodynamic formulation of quantum mechanics is extended to include further densities known in hydrodynamics and their time-evolution.The equations of motion of the complex Bohmian quantities in position space are used to obtain transport equations for complex momentum and energy densities that can be unified with the continuity equation. Separation into real and imaginary parts leads to hydrodynamic equations known in the literature. The same procedure is repeated in momentum space. Finally, the transition from transport equations describing local densities to Euler equations in a frame co-moving with the convection velocity is made.