QUANTUM-STATISTICAL FOUNDATION TO THE FERMI-LIQUID MODEL AND GINZBURG-LANDAU WAVE-FUNCTION

Abstract

An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in the k-space is given, starting with a realistic model of a metal including the Coulomb interaction among and between electrons and lattice-ions. The Ginzburg-Landau wave function PSI(sigma)(r), where sigma represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operator n by PSI(sigma)(r) = [r\n1/2\sigma]. A close analogy between supercurrent and laser is indicated.