Suppose I have a system of fermions in the ground state ##\Psi_0##. If I operate on this state with the number operator, I get(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \langle \Psi_0 | c_k^{\dagger} c_k | \Psi_0 \rangle = \frac{1}{e^{(\epsilon_k - \mu)\beta} + 1} [/tex]

which is, of course, the fermi distribution. What if I operate with ##c^{\dagger}_k c_l##, where ##k \neq l##? I.e, what is

[tex] \langle \Psi_0 | c_k^{\dagger} c_l | \Psi_0 \rangle? [/tex]

My hunch says that this is zero, but I'm not sure. This might be obvious.

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# Easy Question About the Number Operator

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