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note
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x.P(y).
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31
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33744589164
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note
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At weak coupling it makes sense to speak about particles in filled shells, which behave much as core electrons in atomic physics, and particles in partially filled, or valence, shells. In first order, we must diagonalize the perturbation W in the degenerate subspace, dropping the filled shells. Since W is a positive semidefinite operator, with vanishing eigenvalue, 0 is necessarily the lowest one. Typically, the first-order solution is a crude approximation to the exact one, but below, when discussing the exact results, we shall demonstrate that many of the qualitative features hold for all U.
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