In the usual description of electrons in metals and superconductors,
the single electron states are assumed to satisfy Bloch's theorem. This is
because the electron-ion interaction is privileged over the electron-electron
interaction. However the theory of hole superconductivity
proposes that in the transition to superconductivity carriers 'undress'
from the electron-ion interaction. I propose here a new basis set to
describe electrons in the superconducting state that does not
satisfy Bloch's theorem but instead is designed to optimize the
electron-electron interaction. The new basis set favors a superconducting
state where a spin current exists and where states near the bottom of the
band become partially occupied, as predicted by the theory of hole
Erratum: Some typographical errors are corrected and three references are added.