Infinite potential barrier

  1. 1. The problem statement, all variables and given/known data

    write the solutions to the S.E in regions x<o and x between o and a

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    2. Relevant equations

    I believe psi(x)= e^ikx+Re^-ikx in x<0
    and psi(x)=Ae^iqx+Be^-iqx for x b/w o and a.

    3. The attempt at a solution
    My question is, since there is complete reflection occuring at x=a, can A=B in region x b/w 0 and a? If so, there will be destructive interference in the region, giving R=1, which is what we are asked to prove in the question. Is this approach of equating coefficients of wave traveling in +-x directions in this region applicable?
     
  2. jcsd
  3. Chegg
    You haven't defined your potential over the domain of x. My guess based on the info given is that the potential V(x) = infinity for regions less than or equal to x = 0 and greater than or equal to x = a.

    To solve for the equations, you must impart the boundary conditions on the general solution for the wave function. So, psi(x) must vanish at x = 0 and x = a. For example, suppose that psi(x) = Asin(kx) + Bcos(kx) is a general solution to the time-independent schrodinger equation. Now, for the potential I expressed in the first paragraph, we must have psi(x) = 0 at x = 0 and x = a. When x = 0, psi(x = 0) = B; therefore choose B = 0, and now psi(x) = Asin(kx). Now fit the wavefunction to x = a: psi(x=a) = 0 = Asin(ka). Under what conditions for k (the angular wavenumber) will the sine term vanish?

    You can apply this idea to your solutions. As a check, verify that your solution satisfies the time-independent schrodinger equation.
     
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