Exact WKB analysis of non-adiabatic transition probabilities for three levels

The Schrodinger equation idpsi/dt = etaHpsi with a large parameter eta and an appropriate 3 x 3 matrix H is studied by the exact WKB method, i.e. WKB analysis based on the Borel resummation. Transition probabilities of solutions of the equation are explicitly calculated with the help of the connection formula for WKB solutions. Since a 3 x 3 system is considered, addition of new Stokes curves is necessary to obtain the correct connection formula (Berk-Nevins-Roberts' observation), and we present a practically useful procedure for finding required new Stokes curves.