Physics , Condensed Matter
Homework
Due Tuesday, th October
Jacob Lewis Bourjaily
Problem 1: Electron in a Weak Sinusoidal Potential1
Consider an electron moving in a one-dimensional periodic potential U (r) = V cos (2r/a). We are to
obtain the eigenene
Physics , Condensed Matter
Homework
Due Tuesday, rd October
Jacob Lewis Bourjaily
Problem 1
Consider a trigonal Bravais lattice generated by the primitive vectors ai for i = 1, 2, 3 such that
ai aj = a2 cos for i = j .
a) We are to determine for what an
Physics , Condensed Matter
Homework
Due Tuesday, th September
Jacob Lewis Bourjaily
Problem 1
We are asked to study the penetration of normally incident, linearly polarizedwith polarization
parallel to the surfaceelectromagnetic radiation into a conduct
Physics , Condensed Matter
Homework
Due Tuesday, th October
Jacob Lewis Bourjaily
Problem 1: Electron in a Two-Dimensional, Weak Sinusoidal Potential
Consider electrons moving in a two-dimensional, weak periodic potential given by
2x
2y
+ cos
,
V (x, y
Physics , Condensed Matter
Homework
Due Tuesday, th November
Jacob Lewis Bourjaily
Problem 1: Phonon Spectrum of a Diatomic One-Dimensional Crystal
Consider a one-dimensional, diatomic crystal composed of atoms of mass M1 and M2 , respectively.
We may s
Physics , Condensed Matter
Homework
Due Tuesday, th December
Jacob Lewis Bourjaily
Problem 1: BCS Mean-Field Theory
The mean-eld BCS Hamiltonian is
H BCS =
k
(nk, + nk, ) + c , c k, + ck, ck, .
k
(1)
k
When the mean-eld ansatz was made to write the Hami
Physics , Condensed Matter
Homework
Due Tuesday, st November
Jacob Lewis Bourjaily
Problem 1: Thermal Expansion of a One-Dimensional Crystal via Anharmonicities
Consider a simple one-dimensional crystal lattice with nearest-neighbour interaction potenti
Physics , Condensed Matter
Homework
Due Thursday, th December
Jacob Lewis Bourjaily
Problem 1: Little-Parks Experiment
Consider a long, thin-walled, hollow cylinder of radius R and thickness d made of a superconductor
subjected to an external magnetic e