Microscopic Theory of Superconductivity

TOR momentum operators by applying projection operators and we form an orthogonal set.For the uniform solution, St=i+ (LkAtg kt+CC).k»0 Noting that the method has a variational aspect, L» need not be taken from the small-oscillation analysis but may be freely chosen to describe average largeamplitude effects.We obtain improved ground-state energy and single-and multiple-excitation spectra.For the solid-like solution, f(x) is periodic.We expand f=pttk pk (x), where fak, altsf=b, pbk, l.Here are a complete set of Bloch tight-binding orbitals for which k takes on values in the first zone; cr labels the zones.For k= 0 the pk are periodic; for k/0 they have a modulating factor.Thus if the linear shift is performed only for the ao, the ground-state expectation values of physical quantities are periodic.If shifts for kAO are required, the expectation value of the correlation operator ceases to be periodic.The connection between the two solutions is seen by referring to the quantum problem of a particle in a well with several minima (or stationary points).Because of the tunnel effect, good approximate wave functions are superpositions of functions appropriate to the classical separate regions.By analogy, we take e=(P(Ã)O'(P) ' G(E) expS, (E) ~expSs(E)C ( gk ) dR.The coeKcients of the linear and quadratic forms depend on R; the integral over R includes a discrete sum;(P(E) and (P(P) are projection operators of total number of particles à with total momentum P. Detailed calcu- lations of properties. of liquid and solid helium based on the present approach are in progress.