ON A GENERAL NONLINEAR SCHRODINGER-EQUATION ADMITTING DIFFUSION CURRENTS

Some fundamental considerations of quantum theory suggest a general, complex nonlinear Schrodinger equation outside the classes most often studied. The equation follows from admitting quantum diffusion currents, so that the probability density satisfies a Fokker-Planck equation; the real diffusion coefficient D yields observable effects dependent on a dimensionless constant GAMMA = Dm/HBAR. The diffusion currents stem from unitary representations of an infinite-dimensional Lie algebra of vector fields and group of diffeomorphisms, earlier proposed to describe nonrelativistic quantum kinematics.