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Generating wave functions from classical trajectory calculations: The divergence of streamlines
Author(s) -
Stodden C. D.,
Micha D. A.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560320726
Subject(s) - eikonal equation , streamlines, streaklines, and pathlines , divergence (linguistics) , trajectory , jacobian matrix and determinant , classical mechanics , physics , wave packet , matter wave , mathematical analysis , mathematics , quantum mechanics , mechanics , quantum , philosophy , linguistics
Wave functions can be written, for short de Broglie wavelengths, in an eikonal form where the preexponential factor relates to the divergence of streamlines. A method is presented to calculate this divergence by generating the Jacobian of a variable transformation along a classical trajectory without requiring the simultaneous integration of adjacent trajectories. For a system with N + 1 degrees of freedom, there are 2( N + 1) 2 differential equations that must be solved simultaneously to generate the trajectories and the Jacobian. Results are presented for a photodissociation cross section calculation in which the eikonal wave functions have been used in the transition integrals.