- 99-362 Setsuro Fujiie, Thierry Ramond
- Exact WKB analysis and the Langer modification, with application to barrier top resonances.
Sep 29, 99
(auto. generated ps),
of related papers
Abstract. The usual first order WKB ansatz fails to describe
the behaviour at the origin of the solutions of the radial Schr\"odinger
equation, due to the presence of a double pole at the origin for the
Following an idea proposed by Langer in 1937, we study
the behaviour of these solutions in a fixed complex vicinity of the origin as $h$ (the Plank constant) goes to 0. Working in the framework of the exact WKB method, we justify in particular rigorously the so-called Langer modification.
As an application we compute the scattering matrix for the radial
Schr\"odinger equation for energies close to a local quadratic maximum of the potential, and give a quantization rule for the associated resonances.
(This paper will appear in the Conference Proceedings
``Toward the exact WKB analysis of differential equations, linear or
non-linear", T.Kawai and Y.Takei eds.)