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USSR Computational Mathematics and Mathematical Physics

Calculation of one-dimensional quantum mechanical scattering

N. N. Kalitkin, Igor D. Rodionov

Published Jan 1, 1975• 1 citation
Publisher
DOI
10.1016/0041-5553(75)90061-0

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The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear systems. The scattering problem is solved exactly, for the case of a harmonic interaction between the fragments. The exact result is used to assess the validity of two different approximations to the scattering process. The adiabatic approximation, which considers that the relative co-ordinate is frozen during the scattering process, is found to be inadequate for this problem. The uncorrelated scattering approximation, which neglects the correlation between the fragments, gives results in accordance with the exact calculations when the scattering energy is high compared to the oscillator parameter.