The Nature of the Cooper Pair - University of Liverpool

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Combining these ideas, v0 = Aω gives F τ M = δωD. Therefore the displacement is δ = F τ Mω D = e2 4πɛ0d 2 d 1 ve MωD Recall the formula for the Debye frequency: ω D = � � 6Nπ2v 3 1/3 where v is the speed of sound in the metal. We can thus estimate the displacement δ. Superconductivity 9 V , .
The displacement then gives us the attractive potential energy: V ≈ − e2 4πɛ0d 2δ. However, the ion will return to the rest position after a time. This time is half of the period of the simple harmonic motion, the period being T = 2π . ωD During the time T/2, the electron travels a distance l = veT 2 Superconductivity 10 πve = . ωD
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: Recall that the Debye frequency ω
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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