The Nature of the Cooper Pair - University of Liverpool

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The electron would therefore leave a trail of deflected ions behind it. This trail that extends for a distance l, and only exists along a narrow tube in between ions. This net positive charge can attraction another electron that happens to be travelling in the opposite direction through this same tube. So there is an attractive potential between two such electrons that extends over the distance l. Superconductivity 11
We shall approximately represent the attractive potential as a function that is constant within the range l: where V (r) = � V0 = −V0 for r < l 0 for r > l e2 4πɛ0d 2δ. We have seen that the potential only exists within a narrow tube, so it is not exactly a spherical potential. However, if two electrons happen to be travelling in opposite directions and pass very close to each other, then the potential has the same effect as a spherical potential, because the electrons do not experience the potential outside of the tube. Superconductivity 12
Page 1 and 2: Statistical and Low Temperature Phy
Page 3 and 4: When an electron passes in between
Page 5 and 6: Using the small change approximatio
Page 7 and 8: The attractive force is the Coulomb
Page 9 and 10: Recall that the Debye frequency ω
Page 11: The displacement then gives us the
Page 15 and 16: We have seen that two electrons mus
Page 17 and 18: ... recall the quantisation conditi
Page 19 and 20: The Schrodinger equation is then of
Page 21 and 22: Here, we just state the solution to
Page 23 and 24: They will start interfering destruc
Page 25 and 26: Using ∆k.ρ = π we can solve for
Page 27 and 28: The bound pair of electrons is the
Page 29 and 30: The number of Cooper pairs is there
Page 31 and 32: So, as in superfluid helium-4, we m
Page 33 and 34: APPENDIX: Solving for the Cooper pa
Page 35 and 36: The attractive potential is very sm
Page 37 and 38: Therefore and sin(kR) = 0, k = nπ
Page 39 and 40: The product of the waves sin(kr) an
Page 41 and 42: Return to the Schrodinger’s equat
Page 43 and 44: So in energy variable, the density
Page 45 and 46: However, ε is 2�ω D, then the u
Page 47 and 48: We have found both aε and ∆. Thi

The Nature of the Cooper Pair - University of Liverpool

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