= Classically forbidden region
{title2=$E<V(x)$}
A <classically forbidden region> would require negative classical <kinetic energy>, but a quantum <wavefunction> need not vanish there. For constant <potential energy>, it is $Ae^{qx}+Be^{-qx}$ with $q=\sqrt{2m(V-E)}/\hbar$. Boundary matching determines both coefficients. Beside a hard wall at $D$, a nonzero forbidden-region solution is proportional to $\sinh[q(D-x)]$, and therefore has no interior <nodes>. Across a finite barrier, both exponentials are generally needed; a pure decaying exponential is appropriate only when the other boundary condition permits it.
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