= Hydrogen ground-state probability beyond the classical turning point
{title2=$P(r>2a_0)=13e^{-4}$}
The nonrelativistic hydrogen ground <energy> is $-e^2/(8\pi\epsilon_0a_0)$. Requiring nonnegative classical <kinetic energy> restricts radius to $r\leq2a_0$. Integrating the quantum ground-state radial <probability density> beyond that radius instead gives $13e^{-4}\simeq0.238$. A bound-state tail can therefore have substantial integrated <probability> outside the classically allowed region without violating <energy> conservation.
Back to article page
