Semiclassical theory for inelastic scattering

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Abstract
We present a simple theory for obtaining the semiclassical approximation for inelastic scattering. The theory gives explicit expressions for the expectation values of a wide class of quantum operators, generally valid up to O(ħ), which may be used to characterize the final distribution of a scattered particle. We illustrate the method with a one-dimensional model consisting of a particle scattering from a harmonic oscillator. In addition, we apply the theory to examine under what conditions the so-called trajectory approximation is and is not valid.