A New Level-Crossing Two-State Model Solvable in Terms of Hypergeometric Functions

We present a new exactly integrable time-dependent constant-amplitude level-crossing two-state quantum model for which the detuning of the excitation laser field varies with time over a restricted interval. This field configuration is a member of one of the eleven independent classes of general Heun two-state models. We prove that this is the only non-classical unconditionally solvable field configuration among the general Heun classes, solvable in terms of finite sums of Gauss hypergeometric functions. Each of the two fundamental solutions that compose the general solution of the problem is written as an irreducible linear combination of two ordinary hypergeometric functions.