The Nature of the Cooper Pair - University of Liverpool

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To develop the idea ... 1. Estimate the attraction between two electrons. 2. Guess a wavefunction for the electron pair. 3. Solve Schrodinger’s equation for the energy. 4. Obtain the wavefunction of the Cooper pair. 5. Explain why a superconductor has zero resistance. (Weisskopf(1979)http://cdsweb.cern.ch/record/880131/files/p1.pdf) Superconductivity 1
When an electron passes in between two positive ions in a metal, it attracts the ions. The ions move closer together, creating a region that has slightly higher positive charge. This creates an attractive potential for other electrons. Superconductivity 2
Page 1: Statistical and Low Temperature Phy
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 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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