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BCS theory gives condensed-matter physics one of its few genuinely load-bearing equations, and it is worth writing down because it exposes a real, falsifiable assumption rather than decorating the prose. In the weak-coupling limit, the transition temperature is related to the strength of the electron-phonon coupling N(0)V (density of states at the Fermi level times the pairing interaction) and the characteristic phonon energy (the Debye frequency) by:
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Equation 3 · Physics
From Origins to Frontier: A History of Quantum and Condensed-Matter Systems
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BCS theory gives condensed-matter physics one of its few genuinely load-bearing equations, and it is worth writing down because it exposes a real, falsifiable assumption rather than decorating the prose. In the weak-coupling limit, the transition temperature is related to the strength of the electron-phonon coupling N(0)V (density of states at the Fermi level times the pairing interaction) and the characteristic phonon energy (the Debye frequency) by: