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Adiabatic series expansion and higher-order semiclassical approximations in scattering theory

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The scattering properties of any complex scattering potential, nu: R -> C, can be obtained from the dynamics of a particular non-unitary two-level quantum system. S-nu. The application of the adiabatic approximation to S-nu yields a semiclassical treatment of the scattering problem. We examine the adiabatic series expansion for the evolution operator of S-v and use it to obtain corrections of arbitrary order to the semiclassical formula for the transfer matrix of S-nu. This results in a high-energy approximation scheme that unlike the semiclassical approximation can be applied for potentials with large derivatives.

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Institute of Physics (IOP) Publishing

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Optics, Transfer matrix

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Journal of Physics A

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10.1088/1751-8113/47/34/345302

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