Transmission Coefficient for Quantum Barrier

  • #1
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Homework Statement



Picture of Problem:

pYca7nE.png


Homework Equations



$$\psi(x) = A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3

The Attempt at a Solution



I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier, after barrier), such that the values of the functions at the barrier edges as well as their derivatives are equal. But i am not sure how to solve for each coefficient. Also how does the length of the barrier, d, come into play?

k is equal to $$\sqrt{\frac{2mE}{\hbar^2}}$$ outside the barrier and $$\sqrt{\frac{2m(E-V)}{\hbar^2}}$$ inside the barier.
 
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Answers and Replies

  • #2
vela
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I know i need to relate the wave functions $$A_n e^{ikx} + B_n e^{-ikx}$$ for n=1,2,3 (the three areas of the barrier - before barrier, inside barrier, after barrier), such that the values of the functions at the barrier edges as well as their derivatives are equal.
Why don't you start by writing down the equations you get?
 

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