- #1
metapuff
- 53
- 6
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
[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.
[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.