**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 - N_{av})^{2}>
is given by:

<(N -
N_{av})^{2}> = 4 å** _{k}** u

where N_{av}
= å** _{k}** n

Using
your knowledge of how _{k}** _{k}**
depend on k, estimate the rms deviation
of the particle number from the mean value, dN

2. BCS Variational Calculation

Starting
from the BCS pairing Hamiltonian in terms of the _{k}** _{k}**,
work through the variational calculation and derive the final results for