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.