MULTISCALE SEMICLASSICAL APPROXIMATIONS FOR SCHRODINGER PROPAGATORS ON MANIFOLDS Academic Article uri icon

abstract

  • Exponential representations of the Schrdinger propagator are constructed for an interacting quantum system on a semi-Riemannian manifold M. For a local fundamental solution of the time dependent Schrdinger equation, the higher-order WKB approximation is re-expanded in the scaling parameter responsible for the gauge invariant derivative expansion. The geometrical methods which establish the consistency between the WKB and expansions involve a perturbative analysis of the classical dynamics on M which employs the Green function of the inhomogeneous geodesic deviation equation. The analysis applies when both propagator arguments lie in a region which is convex with respect to the classical motion. A multi-scale analysis in the parameters h{stroke}, , charge and time displacement t is performed, leading to simple basic coefficient functions and their recurrence relations. These propagator representations display explicitly the interplay between the local geometry of the manifold and the effects of the background electromagnetic fields. 1992.

published proceedings

  • ANNALS OF PHYSICS

author list (cited authors)

  • MOLZAHN, F. H., OSBORN, T. A., & FULLING, S. A.

citation count

  • 7

complete list of authors

  • MOLZAHN, FH||OSBORN, TA||FULLING, SA

publication date

  • February 1992