The Nature of the Cooper Pair - University of Liverpool

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So if the distance between the electrons is smaller than the wavelength of each electron, then the angular momentum would be zero. In a simplistic way, we may imagine the the electron pair move against each other along very close, parallel paths, and that they equally likely to do so in any direction. That is, the wavefunction should be spherically symmetric. Superconductivity 17
The Schrodinger equation is then of the same form as that for the the ground state electron of the hydrogen atom: − �2 1 2µ r2 d R dr � r 2dR dr � + V (r)R = ER. except that the electron mass is replaced by µ, the reduced mass me/2. We need to use this reduced mass because both electrons are moving, unlike a hydrogen atom in which the nucleus is approximately stationary. http://en.wikipedia.org/wiki/Reduced_mass To show that a bound state is possible, we need to solve this equation to see if the wavefunction has a finite size. Superconductivity 18
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: ... recall the quantisation conditi
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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