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We consider an exact population transition, defined as the probability offinding a state at a final time being exactly equal to the probability ofanother state at the initial time. We prove that, given a Hamiltonian, therealways exists a complete set of orthogonal states that can be employed astime-zero states for which this exact population transition occurs. The resultis general: it holds for arbitrary systems, arbitrary pairs of initial andfinal states, and for any time interval. The proposition is illustrated withseveral analytic models. In particular we demonstrate that in some cases, bytuning the control parameters a \textit{complete} transition might occur, wherea target state, vacant at $t=0$, is fully populated at time $\tau$.

Universality in Exact Quantum State Population Dynamics and Control