A special case occurs where a system oscillates between two unstable levels that have the same life time τ τ . If atoms are excited at a constant, say n/time, to the first state, some decay and the rest have a probability P 12 to transition to the second state, so in the time interval between t and (t + dt) the number of atoms that jump to the second state from the first is n ( 1 − − e − − t / τ τ ) P 12 d t , so at time t the number of atoms in the second state is