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

[spaghettibretty]

Homework Statement

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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, L_x, equals 2.02e-10 m. Likewise, the longer side, L_y equals 2.77e-10 m.

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

Homework Equations

E = n^2 * h^2 / (8*m*L^2)
E_{x, y} = n_x^2 * h^2 / (8 * m * L_x^2) + n_y^2 * h^2 / (8 * m * L_y^2)

The Attempt at a Solution

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All I need to know are the constants, n_x and n_y, 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 n_x = 3 and would n_y = 4?

 

[Greg Bernhardt]

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?