- 99-39 Alexander Fedotov and Frederic Klopp
- A complex WKB method for adiabatic problems
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Feb 1, 99
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Abstract. This work is devoted to a new version of the complex WKB method
suited for adiabatic perturbations of one-dimensional periodic
Schr{\"o}dinger operators. Therefore we introduce an additional
parameter and it is this parameter (and not the variable of the
equation) that will become complex. This naturally leads to
canonical domains where we construct solutions of the Schr{\"o}dinger
equation with a standard asymptotic behavior. These can be used to
compute the asymptotics of the exponentially small coefficients of
transfer matrices (e.g. scattering matrices, monodromy matrices,
etc). We give an example of such a computation.
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