University of California, Berkeley
Physics 141b
Homework Assignment #8
1. Consider a pair of electrons in a singlet state, described by the symmetric spatial wave
function
ik( r r ')
d 3k
(r r ' ) =
(
k
)e
(2 ) 3
In the momentum representation the Sc
University of California, Berkeley
Physics 141b
Homework Assignment #7
1. Magnetic field penetration in a plate. The penetration equation may be written as
2 2 B = B , where is the penetration depth.
(a) Show that B(x) inside a superconducting plate perpe
University of California, Berkeley
Physics 141b
Homework Assignment #3
1. For a ferromagnet at low temperature, it is a fair approximation to define the
annihilation and creation operators a and a+ at lattice site j as (Holstein-Primakoff
S jx + iS jy
S j
University of California, Berkeley
Physics 141b
Homework Assignment #1
1. Interface Plasmons. We consider the plane interface z=0 between metal 1 at z>0 and
metal 2 at z<0. Metal 1 has bulk plasmon frequency p1 ; metal 2 has plasmon
frequency p 2 . The di
University of California, Berkeley
Physics 141b
Homework Assignment #4
1. An alternative way to view the Hartree-Fock equation is to work directly on the wave
function of N electron system instead of working on second-quantization. The
2 2 1
e2
Hamiltonia
University of California, Berkeley
Physics 141b
Homework Assignment #5
1. Assuming there is no free charge and that B=H,
1 2D
2
(a) from Maxwell's equations show that 2
=
E
.
c t 2
(b) for plane waves, show that ( 2 c 2 k 2 )E + 4 2 P = 0 .
1 D
1 B
(a) W
University of California, Berkeley
Physics 141b
Homework Assignment #10
1. Heat capacity of magnons. Use the approximate magnon dispersion relation
= Dk 2 to find the leading term in heat capacity of a three-dimensional ferromagnet
at low temperature. Th