Physics 212 C
HW 2 .1
Presenter : Daniel Rey
Reviewer : Nick Rogers
The EM waves must satisfy the source-free Maxwell s equations,
B=
1
c2
t E,
E = - t B
Introduce a vector potential choosing the divergence free gauge,
B = A , E = - t A
2-
t 2
A = 0.
A
~2 2
~
r+
2m
2m
(z )
=
E
= X ( x) Y ( y ) Z ( z )
X (x) = eikx x
Y (y ) = eiky y
~2
2
k 2 + ky X Y Z ( z )
2m x
00
~2
XY Z (z ) +
2m
k2 =
2
kz = k 2
00
z0
0
0+
dz
2mE
~2
2
kx
2
ky
2
( z ) Z ( z ) = kz Z ( z )
Z (z ) +
(z ) XY Z (z ) = EXY Z (z )
z0 +
(z
L.J. Sham
April 4, 2013
Physics 212C Homework Set 1
1. The Stern-Gerlach experiment
(a) Show that the reduction of the Hamiltonian H to Hamiltonian in the interaction picture
Hi , with the Hamiltonians given by,
p2
I B y y + B (B0 I + z ) z ,
2m
p2
=
I
Alan Chang. Homework 1.
0.1
a
1
|1 = |+
3
1
1
|2 = |+ + |
2
23
1
1
|3 = |+ |
2
23
Remembering the denition of a composite state and applying it to our combined system X and :
(C ) =
|Xi |j ci,j
ij
And then remembering that the conditional states are dened
Setup of Mach-Zehnder interferometer
Path1:
Path 2:
Path 3:
Path 4:
We can see that with our interferometer set up as such, every path that a photon could take bounces off
of one mirror, and picks up the same phase shift from that mirror. Thus, the only d
Quantum HW Solution
Dave Vidmar
May 3, 2013
Problem 2.4
a) We know that the time evolution operator is proportional to the exponential
of the Hamiltonian, as such:
| (t) = eiHt | (0) .
We also know that for a particle in a magnetic eld, the Hamiltonian is
L.J. Sham
4/17/2013
Physics 212C Homework Set 3
1. Correlation between two distant photons
References:
(a) Experiment proposed: J. D. Franson. Bell inequality for position and time. Phys. Rev.
Lett. 62, 2205 (1989).
(b) Experiment: P. G. Kwiat, A. M. Stei
L.J. Sham
4/10/2011
Physics 212C Homework Set 2
1. Quantization of the electric eld and the vector potential Let Ak (r, t) denote the vector
potential of a single normal mode of the classical EM wave with wave vector k and polarization at position r and t
Raul Herrera
PHYS 212C
Spring 2013
HW #3, Problem 1
Fransons Energy-Time Two Photon Correlation Experiment
In 1989 J.D. Franson proposed in a theoretical paper an experiment that was
different from many that had been performed up to that point. The purpos