Off-diagonal two-state impulse
= Off-diagonal two-state impulse
A Hermitian impulse $U\delta(t)$ with zero diagonal has kick operator $e^{-iU/\hbar}$. If $u=U_{21}$, its transition <probability> is $\sin^2(|u|/\hbar)$, reducing to $|u|^2/\hbar^2$ for a weak impulse. The integrated operator has action units, and a pulse integrated across its full support has no extra half-delta factor.