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k, k', alpha and beta are known constants.

[tex] A + B = C + D [/tex]

[tex] k(A-B) = k'(C-D) [/tex]

[tex] Ce^{\alpha} + De^{-\alpha} = Fe^{\beta} [/tex]

[tex] k'Ce^{\alpha} - k'De^{-\alpha} = kFe^{\beta} [/tex]

alpha is ik'L, beta is ikL, k is [tex] \frac{\sqrt{2mE}}{\hbar} [/tex] and k' is [tex] \frac{\sqrt{2m(U_{0}+E)}}{\hbar} [/tex]

Now, I can eliminate F by multiply the 3rd equation by k and setting the two equations equal.

I'm trying to solve for B.

Anybody got an idea where to start? (If you're interested, these are the smoothness conditions of a quantum potential barrier)