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Derivation of the BCS Hamiltonian

Physics Asked by user220348 on February 24, 2021

$$
hat{H}_{mathrm{BCS}}=sum_{k sigma} varepsilon_{k} c_{k sigma}^{dagger} c_{k sigma}-sum_{k k^{prime}} G_{k k^{prime}} c_{k uparrow}^{dagger} c_{-k downarrow}^{dagger} c_{-k^{prime} downarrow} c_{k^{prime} uparrow}
$$

Any books on how to derive it?

I get that the first part is the Hamiltonian of an electron and the second describes the creation of Cooper pairs, but the text I’m reading simply gives it and I was wondering how was it derived, I can’t seem to find a satisfactory online text.

One Answer

I used the pdf that you get when you search on google for the following: "Second-quantization representation of the Hamiltonian of an interacting electron gas in an external potential"

Answered by Audrique on February 24, 2021

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