The Nature of the Cooper Pair - University of Liverpool

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In a simple harmonic motion with amplitude A and frequency ω, the maximum velocity at the rest position is v0 = Aω. This maximum frequency would the velocity of the ion as it takes off immediately after the kick, so v0 = where M is the mass of the ion. The amplitude A corresponds to the displacement δ that we want to find. The frequency ω would be the Debye frequency. Superconductivity 7 F τ M
Recall that the Debye frequency ω D is the maximum vibrational frequency in a lattice. This happens when the ion spacing is equal to a half wavelength: Compare this with the picture of the ions attracted by a passing electron: In both cases, the electron cloud in between would be deformed in the same way. We can expect the same restoring forces on the ions, and therefore the same frequency. Superconductivity 8
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: The attractive force is the Coulomb
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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