Resonant transmission through a square well
= Resonant transmission through a square well
{title2=$T=[1+(q^2-k^2)^2\sin^2(qa)/(4k^2q^2)]^{-1}$}
For an attractive <finite square well> of width $a$, outside wave number $k$ and inside wave number $q$, matching the <wavefunction> and its first <derivative> at both endpoints gives the displayed <transmission probability>. It equals one when $qa$ is an integer multiple of $\pi$: the internal reflections cancel. For $q=2k$ the coefficient of $\sin^2(qa)$ is $9/16$.