Unified semiclassical theory for the two-state system: Analytical solutions for scattering matrices

Chaoyuan Zhu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Unified semiclassical theory is established for general two-state system by employing an exactly analytical quantum solution [C. Zhu, J. Phys. A29, 1293 (1996)] for the Nikitin exponentialpotential model which contains the two-state curve crossing and noncrossing cases as a whole. Analytical solutions for scattering matrices are found for both three- and two-channel cases within the time-independent treatment. This is made possible by introducing a very important parameter d(R0) = √l + 4V122(R0)/[V22(R0) - V11(R0)]2 (V11(R), V22(R) and V12(R) are diabatic potentials and coupling, R0 is real part of complex crossing point between two adiabatic potentials) which represents a type of nonadiabatic transition for the two-state system. For instance, d=∞ represents the Landau-Zener type and d=√2 represents Rosen-Zener type. Since d(R0) runs from unity to infinity, this parameter provides a quantitative description of nonadiabatic transition. The idea used here is the parameter comparison method which makes a unique link between the model and general potential system at the complex crossing point. This method is testified not only by numerical examples, but also by agreement of the present semiclassical formulas with all existing semiclassical formulas.

Original languageEnglish
Pages (from-to)4159-4172
Number of pages14
JournalJournal of Chemical Physics
Issue number10
StatePublished - Sep 1996

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