 Solution

The original PDF threshold contains $\hslash$, not $h$. It is $8E_1$, so the energies strictly above it are exactly those with $n\ge 3$. By the Born rule, the required probability is $1-|c_1{|}^2-|c_2{|}^2$. The two excluded amplitudes areConsequentlyThus, in increasing powers of $1/\pi$,The threshold lies strictly between $E_2$ and $E_3$, so no equality-at-threshold convention affects the answer.