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3. Prove the function
y (x, y,=) = A Sin(
L
Sin(
-)Sin(
:)
L,
L,
x,
satisfies the Schrodinger's equation for a quantum dot with a width of Lx, Ly,
and Lz, and the particle energies are,
n.
E, =
2m
L L
L
with n,,n.,n, = 1,2,3,...

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