Transformation theory and translation factors in inelastic atomic collisions

Details Transformation theory and translation factors in inelastic atomic collisions Transformation theory and translation factors in inelastic atomic collisions

Apr 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977phrva..15.1459s&link_type=abstract

Physical Review A - General Physics, 3rd Series, vol. 15, Apr. 1977, p. 1459-1468. NSF-Navy-NASA-supported research.

Mathematics

18

Atomic Collisions, Coordinate Transformations, Inelastic Collisions, Operators (Mathematics), Schroedinger Equation, Asymptotic Methods, Time Dependence, Translational Motion, Tumbling Motion, Wave Scattering

Scientific paper

It is shown through the use of transformation theory that unique semiclassical atomic scattering states which obey the asymptotic conditions of formal scattering theory can be derived by transforming 'nontraveling' atomic states, ie., states whose coordinate variables are referred to a stationary origin, to frames at rest with respect to the incoming or outgoing particles. An overview of the problem of properly defining such scattering states is presented. The operator which carries out the necessary transformation from inertial to noninertial frames is derived and its properties are discussed. The relation of this transformation operator to the 'translation factor' discussed in the literature is presented. The application of this operator to transform the time-dependent Schroedinger equation from an inertial to a noninertial frame is presented and shown to introduce new terms in the resulting equation. The implications of these new terms to scattering problems are discussed.

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