一维光滑势的散射：在WKB和Born近似之间
Scattering by one-dimensional smooth potentials: between WKB and Born approximation
摘要：
本文讨论了WKB近似和Born（小扰动）近似在量子粒子和经典波被振幅小于入射粒子能量的一维光滑势后向散射（势垒上散射）问题中的适用性。确定性和随机电位被认为是。研究了反射系数和局域化长度与散射势的振幅和纵向尺度的关系。结果表明，微扰理论和WKB理论在势垒上后向散射问题中是不一致的。不仅解决方案，但这两种方法的有效性区域，以及强烈依赖于潜在的配置文件的细节，并为每个潜在的个人。一个简单的标准，允许确定WKB和玻恩近似的适用域之间的边界。
英文摘要：
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with amplitudes small compared to the energy of the incident particle (above-barrier scattering). Both deterministic and random potentials are considered. The dependence of the reflection coefficient and localization length on the amplitude and the longitudinal scale of the scattering potential is investigated. It is shown that perturbation and WKB theories are inconsistent in the above-barrier backscattering problem. Not only the solutions but the regions of validity of both methods as well depend strongly on the details of the potential profile, and are individual for each potential. A simple criterion that allows determining the boundary between the applicability domains of WKB and Born approximations is found.
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