= Solution
Rewrite the real-energy <probability> as $T=[1+U_0^2\sin^2(\zeta a)/(4E(E+U_0))]^{-1}$. Thus $\boxed{T_{\max}=1}$ at $\zeta a=j\pi$, namely $E_j=\hbar^2j^2\pi^2/(2ma^2)-U_0\geq0$, with a strictly positive <resonance (chemistry)>[resonance] <energy> in the ordinary scattering problem. Between <resonance (chemistry)>[resonances] it is less than one and its <Oscillation>[oscillations] approach one as <energy> increases. Generically $T(0^+)=0$; a well tuned to a zero-energy <resonance (chemistry)>[resonance] instead has $T(0^+)=1$. The original transmission plot in S1 illustrates these maxima for a chosen well, not a universal specified depth.
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