Physics 798S

Superconductivity

Spring 2004

Homework 3

Due March 9, 2004

 

1.      BCS ground state wavefunction: sharpness of the number distribution

Show that the squared deviation of the particle number from the mean <(N - Nav)2> is given by:

<(N - Nav)2> = 4 k uk2 vk2

where Nav = k nks

Using your knowledge of how uk and vk depend on k, estimate the rms deviation of the particle number from the mean value, dNrms/N.

 

2.      BCS Variational Calculation

Starting from the BCS pairing Hamiltonian in terms of the uk and vk, work through the variational calculation and derive the final results for uk, vk, and the zero temperature gap D.