Strong-Coupling Limit in the Theory of Superconductivity

Abstract

The Hamiltonian used by Bardeen, Cooper, and Schrieffer in their theory of superconductivity is studied in the strong-coupling limit. The complete set of energy levels can be found by using group theory, even for a finite system. An expression for the grand partition function can immediately be written down, and this expression can be evaluated in a simple manner for a large system. The results are in qualitative agreement with the weak-coupling theory, and in quantitative agreement with the strong-coupling limit of the expressions derived by Bardeen, Cooper, and Schrieffer. The second-order phase transition is a simple consequence of the form of the grand partition function. There is an energy gap independent of the total number of particles which goes to zero as the temperature approaches the critical temperature. The normal state is not metastable below the critical temperature.