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QM Free Particle Approaching Infinite Barrier

  1. Oct 6, 2008 #1
    Solved... i think. It's just Psi(x) = B sin kx

    1. The problem statement, all variables and given/known data
    Consider a free particle psi(x) = A*e^(ikx) approaching an infinite barrier from the left:
    V = 0, x < 0 and V = oo, x >= 0. For this problem use only the time-independent
    Schrodinger Equation.
    a. Find the probability of being reflected from the barrier (recall that energy
    must be conserved).
    b. Find the total wavefunction Psi(x) for x < 0.

    2. Relevant equations

    Schroedinger's equation.

    3. The attempt at a solution

    Okay, solving the wave equation gives the general solution

    psi(x, 0) = A e^(ikx) + B e^(-ikx).

    We know that Psi(x, 0) = 0 when x >= 0, since E < V = oo for all values of E. Part a asks to find the reflection coefficient using conservation of energy, but I did it this way:

    Psi must be continuous at x = 0. Thus A + B = 0, implying that A = -B. Thus the reflection coefficient is 1. This also reduces psi(x, 0) = A sin kx.

    However, I'm a little confused as to how to find Psi(x). My original work was that Psi(x) = integral(-oo to oo) phi(k) A sin kx dk

    but my professor said that due to the conservation of energy, there are only so many allowed energy states. I'm a little confused about this. Is Psi(x, 0) = A e^(ikx) - A e^(-ikx)?

    Any hints would be greatly appreciated. Thanks!
     
    Last edited: Oct 6, 2008
  2. jcsd
  3. Oct 7, 2008 #2

    Avodyne

    User Avatar
    Science Advisor

    Yep, that's it!
     
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