The paper investigates the possibility of obtaining improved eigenfunctions of the reduced Bardeen-Cooper-Schrieffer-Hamiltonian by forming linear combinations of the approximative BCS-functions. For the groundstate an admixture of states with two excited pairs is considered. This leads to a lowering of the ground-state by an amountδW which is independent of the volume and of the same order of magnitude as the energy-gap 2ɛ0. The same shift is produced for the states with excited single-pairs. Superposition of states with one excited pair leads to an additional discrete level within the energy-gap.
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