= Solution
An impulse integrated across its full support produces the <impulsive quantum kick> $K=e^{-i\hat U/\hbar}$. Thus the leading transition amplitude is $-iU_{21}/\hbar$ and
$$
\boxed{P_{1\to2}=\frac{|U_{21}|^2}{\hbar^2}+O(|U_{21}/\hbar|^4).}
$$
Here $U_{21}$ has units of action. The <off-diagonal two-state impulse> is exactly $P=\sin^2(|U_{21}|/\hbar)$ for a Hermitian two-state impulse with zero diagonal. No <energy> denominator occurs: the impulse is instantaneous.
Back to article page
