Quantum-Hydrodynamic Analogy

摘要

Classical quantum theory (see [1]) has drawn attention to the analogy between barotropic motions of an ideal compressible fluid and the quantummechanical states satisfying the Schr?dinger equation (further, for scaling the coordinates, we put m = 1). We make the replacement (E. Madelung, 1929) and, as a result, obtain the set of equations Set (2) can be interpreted as the equations of barotropic motions of a compressible fluid, where ρ is the fluid density and S is the velocity potential. The first equation of set (2) is the continuity equation, and the second equation is the Cauchy–Lagrange integral in the case of the external field of forces with the potential V. The term is the specific quantummechanical potential, which replaces the pressure function in this case.