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# Fermi Surface and Orthogonality Catastrophe

1. ### Morberticus

81
I am reading section 8.5.1 of this book (page 442 of the book, page 465 of the pdf). The author claims the discontinuous jump in the occupation number is of size Z, where

$Z = |\langle 0,N+1|a^\dagger |0,N\rangle|^2 = |\langle 0,N-1|a |0,N\rangle|^2$

I.e. Z is the probability that the system will be in an N+1 (N-1) ground state after an electron is added (removed). They say this follows from equation 8.123 but I don't find it obvious how. Is there an easy logical path from equation 8.123 to the above relation?

Last edited: Jun 20, 2014
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### Staff: Admin

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

4. ### rigetFrog

112
post equation 8.123 for us

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