The Nature of the Cooper Pair - University of Liverpool

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The potential energy of an electron due to a positive ion is U = − e2 4πɛ0r . This is normally cancelled out by the free electrons. If an ion is displaced, the change in the potential is the attractive potential that now appears. This may be estimated by the small change approximation: δU ≈ dU dr δr. Superconductivity 3
Using the small change approximation, the attractive potential is V ≈ − e2 4πɛ0d 2δ where r is roughly the distance d between ions, and δ is the displacement of the ion. To estimate δ, consider the ion next the electron path. Superconductivity 4
Page 1 and 2: Statistical and Low Temperature Phy
Page 3: When an electron passes in between
Page 7 and 8: The attractive force is the Coulomb
Page 9 and 10: Recall that the Debye frequency ω
Page 11 and 12: The displacement then gives us the
Page 13 and 14: We shall approximately represent th
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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