The Nature of the Cooper Pair - University of Liverpool

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Let the difference in k be ∆k. The phase at ρ for each sine function is kρ. Since this difference is is π between the maximum and minimum k, so ∆k.ρ = π. To express in terms of E F , we use E = p2 . 2me The small change approximation gives ∆E = p∆p . me At the Fermi energy, and for an energy change ∆E equal to ∆, we have ∆ = p F ∆p me Superconductivity 23 = pF .�∆k . me
Using ∆k.ρ = π we can solve for the size of the wavefunction: ρ = hp F 2me∆ . Putting in typical values, we find the the size of the wavefunction is of the order of 10 −4 cm. This is much larger than the size of an atom. Superconductivity 24
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 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: They will start interfering destruc
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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