Schrodinger lumps

Abstract

Gives a systematic method to construct exact non-spreading wave packed solution (lumps) of the Schrodinger equation for a charged particle in an electromagnetic field and of the nonlinear Schrodinger equation. The method yields new kinds of accelerating lumps with both rotational and translational motion, in contrast to the more familiar soliton solutions which have constant velocity. In particular, the authors find new normalisable coherent states for the harmonic oscillator and new normalisable lumps for a charged particle in a constant magnetic field plus an electric field with axial symmetry. The method can be applied to relativistic wave equations and classical field theories to find their lump solutions.