I-J-5 Exact Analytical Solution of the N-Level Landau-Zener Type Bow-Tie Model

Valentine N. OSTROVSKY (Univ. St. Petersburg, Russia and IMS) and Hiroki Nakamura

[J. Phys. A. 30, 6939 (1997)]

The non-stationary Schrödinger equation in finite basis of states is considered for the Hamiltonian matrix linearly depending on time. Exact analytical solutions of asymptotic transition probabilities are obtained for a bow-tie model, in which an arbitrary number of linear time-dependent diabatic potential curves cross at one point and only a particular horizontal curve has interactions with the others. Based on the contour integral method used, some mathematical aspects such as a possible generalization of the Whittaker functions are also briefly discussed.


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