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Neitrino
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/nbo10 said:Some of the statements in post #7 are confusing and seem to be incorrect. The wording could be the reason that they seem to be incorrect.
(*Start a unimportant detail*).reilly said:The hardest part of the BCS theory, at least in my opinion, was showing that electrons near the Fermi Surface attracted rather than repelled each other. They reasonably assumed that the electron-electron potential near the Fermi Surface was constant in momentum space. This means that the potential is given by a huge matrix of 1s, multiplied by -V, the potential (V>0).
reilly said:Constant throughout momentum space means concentrated in configuration space. -- its like a very strong negative potential centered at X=0.
reilly said:So, roughly speaking, this hole can suck all the electrons into itself, and creates a bound state, which involves all the electrons.
reilly said:The other solutions, give particle-like states; Cooper Pairs in particular, with positive excitation energies. Further, the ground state has every possible electron state filled, so the only excitations possible are hole-electron pairs, which due to the positive excitation energy (energy gap) behave like 'free particles'" .
The BCS approximation, also known as the Bardeen-Cooper-Schrieffer theory, is a theoretical framework in condensed matter physics that describes the behavior of superconductors. It explains how electrons interact with each other to form pairs, known as Cooper pairs, which are responsible for the phenomenon of superconductivity.
The BCS approximation is based on the concept of electron-phonon interactions, where electrons interact with the vibrations of the crystal lattice. This leads to a decrease in the energy of the electrons, making it more favorable for them to form pairs and move through the material without resistance.
The main assumptions of the BCS approximation are that the electrons in the superconductor behave as a Fermi gas, where they occupy energy levels up to a certain energy called the Fermi energy. It also assumes that the electron-phonon interaction is responsible for the formation of Cooper pairs and that the pairs behave as bosons rather than fermions.
The BCS approximation is a mean-field theory, which means it does not take into account the effects of quantum fluctuations and disorder. It also does not explain high-temperature superconductivity, which occurs in materials with complex crystal structures and strong electron-electron interactions.
The BCS approximation provides a comprehensive explanation for the phenomenon of superconductivity and has been successful in predicting and explaining many of its properties, such as the critical temperature and the energy gap. It also serves as the basis for other theories that try to explain superconductivity in different types of materials.