An Initial BoundaryValue Problem for the Schrodinger Equation with Long Range Potential
Abstract
We consider the exterior Dirichlet problem in R^3 for the Schrodinger equation with a Coulomb potential. For such a Schrodinger equation defined in all of R^3, the socalled reference problem, a fundamental solution is known in terms of Whittaker functions and the appropriate radiation conditions and the asymptotic behaviour of solutions can easily be obtained. Consequently, we can prove the limiting absorption principle, establish the existence of solutions to exterior boundaryvalue problems and show that the associated wave operators exist. This then enables questions concerning the asymptotic behaviour of time dependent solution of the exterior problem to be resolved in terms of the reference problem.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 June 1988
 DOI:
 10.1098/rspa.1988.0065
 Bibcode:
 1988RSPSA.417..353L