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The BCS results for the superconducting gap $\Delta$ and $T_C$ are obtainedfrom a one-particle model. Superconductivity appears when the electronic energygains of the band structure surpass the energy needed for atomic vibrations ormagnetic moment oscillations. The vibration/oscillation amplitudes determinethe superconducting gap, and the Fermi surface is important for theq-dependence. This permits for complementary interpretations of the parametersfor superconductivity and modeling of density-of-state effects. It also makesthe superconducting mechanism less exotic.

Mechanisms for the superconducting state from a one-particle derivation of the BCS gap equations