1. The problem statement, all variables and given/known data
We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by
\(\psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L) \)
\(\psi(x) = \psi(x + L)\)
What is the density of states at the Fermi level for this metal?
3. The attempt at a solution
According to my book, the total energy of the system is
\(E = \frac{\hbar^{2}\pi^{2}n^{2}}{2mL^{2}}\)
why is this?
It's evident that k = n*2*pi because of the boundary contidions. I don't know what to do next.
We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by
\(\psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L) \)
\(\psi(x) = \psi(x + L)\)
What is the density of states at the Fermi level for this metal?
3. The attempt at a solution
According to my book, the total energy of the system is
\(E = \frac{\hbar^{2}\pi^{2}n^{2}}{2mL^{2}}\)
why is this?
It's evident that k = n*2*pi because of the boundary contidions. I don't know what to do next.
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