This IMA Volume in Mathematics and its Applications QUASICLASSICAL
METHODS is based on the proceedings of a very successful one-week
workshop with the same title, which was an integral part of the
1994-1995 IMA program on "Waves and Scattering." We would like to
thank Jeffrey Rauch and Barry Simon for their excellent work as
organizers of the meeting. We also take this opportunity to thank
the National Science Foun dation (NSF), the Army Research Office
(ARO) and the Office of Naval Research (ONR), whose financial
support made the workshop possible. A vner Friedman Robert Gulliver
v PREFACE There are a large number of problems where qualitative
features of a partial differential equation in an appropriate
regime are determined by the behavior of an associated ordinary
differential equation. The example which gives the area its name is
the limit of quantum mechanical Hamil tonians (Schrodinger
operators) as Planck's constant h goes to zero, which is determined
by the corresponding classical mechanical system. A sec ond example
is linear wave equations with highly oscillatory initial data. The
solutions are described by geometric optics whose centerpiece are
rays which are solutions of ordinary differential equations
analogous to the clas sical mechanics equations in the example
above. Much recent work has concerned with understanding terms
beyond the leading term determined by the quasi classical limit.
Two examples of this involve Weyl asymptotics and the large-Z limit
of atomic Hamiltonians, both areas of current research."
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