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What is the energy of the following state (quantum square)?

  1. Nov 7, 2014 #1
    1. The problem statement, all variables and given/known data

    What is the energy of an STM tunneling electron in the following state? This "quantum square" model can be seen as a "particle in a 2-D box" problem.
    <Refer to the picture below>
    The protrusions are Fe atoms and the surface is Cu(111).
    Given that the radius of an Fe atom is 126 pm (1.26e-10 m), I've calculated that the shorter side, Lx, equals 2.02e-10 m. Likewise, the longer side, Ly equals 2.77e-10 m.

    Lx = 2.02e-10 m
    Ly = 2.77e-10 m
    h = Planck's constant = 6.626e-34 J*s
    m = effective mass of an electron in this scenario = 0.38me = 0.38 * 9.109e-31 kg = 3.461e-31 kg

    Jy6Ory4.png
    2. Relevant equations

    E = n^2 * h^2 / (8*m*L^2)
    Ex, y = nx^2 * h^2 / (8 * m * Lx^2) + ny^2 * h^2 / (8 * m * Ly^2)

    3. The attempt at a solution

    All I need to know are the constants, nx and ny, the rest of the problem would just be a plug and chug. Although, I don't think the number of Fe atoms represent the n constants. I believe that the number of nodes + 1 would give me the values I need, but I'm not quite sure what in this picture represents the nodes. Do the black dots in the square represent the nodes? Or do they represent the actual n values? If they represented the n values, would nx = 3 and would ny = 4?
     
  2. jcsd
  3. Nov 12, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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