PHYSICS 295B: Quantum Theory of Solids: Lec15. BCS theory of superconductivity

[@dgwparfitt]

Could you please explain why the phase in the BCS wavefunction is independent of k? I have never managed to find an explanation for this in any of the books on superconductivity.

[@andrewhardy8926]

In general you only impose a global gauge constraint, but see the end for discussion about plasmons for spatially varying theta fluctuations

[@catmyc]

An easy way to see it is to look at the original wave function g(r1-r2) chi_{12}. This phase in the BCS wavefunction is just a global phase in front of g(r1-r2). A global phase does not change your quantum state. Remember where u_k and v_k come from ? Just by redefining g(k) = v_k / u_k. The phase with v_k is infact the phase of g(k).