- #1
joex444
- 44
- 0
Got 4 equations with 4 unknowns and I'm being a retard so I can't figure this thing out.
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)
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)