Adiabatic Series Expansion and Higher-Order Semiclassical Approximations in Scattering Theory
arXiv:1402.6458 · doi:10.1088/1751-8113/47/34/345302
Abstract
The scattering properties of any complex scattering potential, v:R -> C, can be obtained from the dynamics of a particular non-unitary two-level quantum system S_v. The application of the adiabatic approximation to S_v 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 v. This results in a high-energy approximation scheme that unlike the semiclassical approximation can be applied for potentials with large derivatives.
7 pages
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Cited by in corpus (5)
- Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
- Transmission of low-energy scalar waves through a traversable wormhole
- Dynamical formulation of low-energy scattering in one dimension
- Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians
- Composition of Transfer Matrices for Potentials with Overlapping Support