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Equation 3 · Part 1 · From Origins to Frontier: A History of Quantum and Condensed-Matter Systems

Symbol omega_D

ℏωD\hbar\omega_D
ωD\omega_D

What this part means

the because.

Its job in the formula

omegaDa_D is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

The formula also predicts an upper ceiling: no phonon-mediated superconductor should exceed roughly 30–40 kelvin, because ωD\omega_D for any real lattice is bounded.

The passage around this formula

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 TcT_c 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 ℏ\hbarωD\omega_D (the Debye frequency) by:

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Sources cited in the article section

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