Quantum hydrodynamics

Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems (usually quantum tunnelling). They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the Wigner–Boltzmann equation. In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrödinger equation by way of Madelung equations.