We derive an algorithm to calculate quantum transmission and reflection amplitudes (S‐matrix elements) for rearrangement reactions using the invariant imbedding method. Our approach can incorporate closed channels, treat complex potentials (to simulate decay), and can be used within an adiabatic representation (in which derivative coupling terms are present) or within a diabatic representation. The method can also be used to determine bound‐state energies when only closed channels are present. The method is demonstrated on a rearrangement problem with two coupled potential surfaces (four channels) as a function of energy in the energy region from the lowest channel threshold through the highest channel threshold.
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For example, in one of the problems treated below, the integral over the barrier, is very large, and therefore the linearly independent solutions of the Schrödinger equation, which can be written as linear combinations of become numerically linearly dependent in the numerical propagation of the wave function.
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© 1994 American Institute of Physics.
1994
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