304 SOLUTIONSa) If the initial state is at then the amplitude of the
state for is given by
The last equation is the probability of ending in the state if the
initial state is This expression is valid as long as it is less than 1 or
if
b) The state cannot be reached by a single transition from
since the matrix element However, can be reached by a
two-step process. It can be reached from and is excited from
The matrix element is so we have that
Note that Similarly, one can show that However,
the total probability, when summed over all transitions, cannot exceed 1.
Therefore, we define a normalizedprobability