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••• Use the Heisenberg uncertainty principle to estimate the size of a Cooper pair in indium, where the gap energy is 0.0011 eV and the Fermi energy is 8.6 eV. (Recall that the gap energy is the binding energy of a Cooper pair.) The Cooper pair, consisting of two conduction electrons, has an energy of twice the Fermi energy, reduced by the gap energy. If the Cooper pair is squeezed down from a very large size to a size ∆ x, the momentum must increase by an amount ∆ p given by the uncertainty principle, and consequently the energy will increase by ∆ E − (dE/dp) ∆ p. The energy increase cannot exceed the binding energy, or else the pair will unbind. These considerations allow you to compute the minimum possible size of a Cooper pair.
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