Determine the exact value of the transmission coefficient D for the passage of a particle through a parabolic potential barrier U(x)=−21kx2 (supposing that D is not small) (E. C. Kemble 1935).\dagger
\footnotetext{† The solution of this problem can also be applied to penetration sufficiently near the top of any barrier U(x) whose dependence on x near the maximum is quadratic.}