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irmanbearpig
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Homework Statement
I am trying to find the coefficients in a Schrodinger equation approaching a finite potential.
https://www.physicsforums.com/showthread.php?t=203385
It is a problem similar to this, except a little easier. In my case, though, there is no V1 as shown in the picture at the thread, the potential is at x = 0 and doesn't drop back down, just continues going in the positive x direction. So at x = 0 it just goes straight up vertically, then levels off and keeps going, creating a sort of wall. (hope that is a good enough explanation)
Homework Equations
Schrodingers Equation
The Attempt at a Solution
I have defined the regions as:
Region 1: V(x) = 0 for x < 0
Region 2: V(x) = V0 for x > 0
I have used Schrodinger's Equation to get the wave function for each region:
Region 1:
Psi(x) = Aeik1x + Be-ik1x
With A being the incident wave and B being the reflected wave off of the potential barrier.
I also have K1 = (2mE/h2)1/2
Region 2:
Psi(x) = Ceik2x
With C being for the continuing wave, there is no reflected wave here because region 2 contains the barrier. I also think C would be considered T (transmitted).
I also have K2 = (2m(E-V0)/h2)1/2
So I can say that A + B = C at x = 0 (I think). I can also say that their derivatives are equal at that point, so ik1A - ik2B = ik2C
I also know that 1 = P(R) + P(T)
and R = abs(B2/A2)
and I have written T = 1 - R
I guess I'm supposed to solve B and C in terms of A, I'm almost positive all of the information thus far is correct, unless I just typed something incorrectly.
It's something that I haven't ever seen/done before so I'm absolutely stumped... I even looked at some old physics books from the library trying to get some ideas but am lost. I'm sure it's something really simple... I just need to know where to go from this point in order to solve for A B and C.
Thanks!
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