ABSTRACT
This chapter investigates the meaning of the phase of the pair function, and shows that phase and pair number are conjugate operators which exhibit an uncertainty relation. It considers the question of the supercurrent density. The chapter also considers the simplest case of boson superfluids such as superfluid helium, and then for electron pairs in the bcs context, introducing the pair function, an effective two-particle wavefunction for the pairs. It finds that a current of pairs carries along with it other contributions to the supercurrent, and shows how to calculate using bcs theory the total supercurrent and hence the effective amplitude of ψ. When performing calculations on superfluid systems it is most convenient to work with the states of definite phase which are diagonally ordered. The 'supercurrent' means simply the total current carried by the system when the excitations are in equilibrium under scattering for the given value of s.
