A theory of electron scattering by potential with slow spatial variation in one-dimensional systems is proposed. It takes into account the perturbation of all order taking advantage of the long range nature of the potential. The theory is extended to the case of random potential and good agreements with the numerical calculation are obtained for wide range of parameters, while the precision of Born approximation becomes rapidly worse if the correlation length of the potential exceeds the wave length of the electron. As an application, the mobility of quantum wires limited by the surface roughness scattering is discussed.
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Arisato Kawabata (1992) studied this question.
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