Abstract
We study the well-known problem of 1-d quantum scattering by a potential barrier in the semiclassical limit. Using the so-called exact WKB method and semiclassical microlocal analysis techniques, we get a very precise and complete description of the scattering matrix, in particular when the energy is very close to a unique, quadratic maximum of the potential. In our one-dimensional setting, we also recover the Bohr-Sommerfeld quantization condition for the resonances generated by such a maximum.
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Ramond, T. Semiclassical study of quantum scattering on the line. Commun.Math. Phys. 177, 221–254 (1996). https://doi.org/10.1007/BF02102437
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DOI: https://doi.org/10.1007/BF02102437