If the system at t = 0 is in the | ψ ψ k ⟩ ⟩ state, then the probability of finding the system in the | ψ ψ n ⟩ ⟩ state is given by w k n = | η η | 2 2 Ω Ω 2 ( 1 − − cos ⁡ ⁡ 2 Ω Ω t ) which is a periodic function with frequency 2 Ω Ω ; this function varies between 0 and | η η | 2 / Ω Ω 2 . At the exact resonance, i.e., ε ε = 0 , the above formula reduces to w k n = 1 2 ( 1 − − cos ⁡ ⁡ 2 | η η | t )