Schroedinger's Rule and Hydrodynamics

R. Eisenschitz

Mark P. Davidson

The mathematical expression for the electromagnetic current of a quantum particle describes an extended charge in the sense that it is non-vanishing over the volume of the wave packet or the Schroedinger wave for the particle. In the hydrodynamic model this charge current and associated density are interpreted as a physical reality. Coupling such a current to a classical electromagnetic field in the soft photon limit then results in a theory for radiation. It is shown that this predicts that bremsstrahlung is sometimes greatly suppressed when the force acting on the particle is due to a classical potential field and when the volume over which the force is active is small compared to the volume of the particle's wave packet. Solving the same problem using conventional quantum radiation theory gives a different result. Therefore it is possible to test this effect experimentally and either confirm or rule out a hydrodynamic model for Schroedinger wave mechanics. An experiment is proposed to make such a test. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.

Makoto Tsubota, Michikazu Kobayashi, Hiromitsu Takeuchi

Herbert E. Spohn

The lecture notes cover the emergence of generalized hydrodynamics for the classical and quantum Toda chain, the classical Calogero fluid, the Ablowitz-Ladik discretization of the non-linear Schroedinger equation, and the Lieb-Liniger delta-Bose gas. Such diverse models have structurally identical hydrodynamic equations. Added is a comparison with conventional soliton gases.

Miroslav Pardy

The Schroedinger equation with the nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the classical limit of the wave function, the collaps of the wave function and solves the Schroedinger cat paradox.