University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Homework assignment 4
Due Monday November 04, 2013
Problem 4.1. Alice and Bob share two photons in a polarization state whose matrix in the canonical
basis is
3
1
2 i
1 1
1
2i
University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Homework assignment 1
Due Monday September 22, 2013
Problem 1.1. Consider a quarter-waveplate with its optical axis oriented at angle to horizontal.
a) Find the operator assoc
University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Homework assignment 3
Due Monday October 20, 2013
Problem 2.1. Consider two-mode optical state
| =
km |k1 |m2 ,
k,m=0
where subscripts 1 and 2 denote the modes (e.g. state |11
University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Homework assignment 5
Due Monday November 25, 2013
Problem 5.1. Using the Bogoliubov transformation for two-mode squeezing,
S2 ()1 S2 () =
a
S2 ()2 S2 () =
a
a1 cosh a sinh
University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Final examination
December 12, 2013, 8:00 am
Open books. No electronic equipment allowed.
Full credit = 100 points. Attempt all problems. Partial credit will be given.
Problem
Problem 3.1.
=
a) 12
= Tr2 12
1 =
b) click
=
k , k , m , m
k , k , m
*
k m k k
km
1 (1 )
m=0
= Tr2 ( 12 click )
=
1
=
c) 1
*
km k m k k m m
k , k , m
kk mm
m
m m
k , k , m
*
k m 1 (1 ) m k k
km
1 (1 ) m k k
Problem 3.2
P
2 hbar c
f
lambda
1, f
0
1
Problem 1.1
In[1]:=
KetPhi Cos, Sin; KetPiOver2PlusPhi Sin, Cos;
a)
In[2]:=
A Simplify
OuterTimes, KetPhi, KetPhi OuterTimes, KetPiOver2PlusPhi, KetPiOver2PlusPhi;
A MatrixForm
Cos2 Sin2
Out[3]/MatrixForm=
1 Cos Sin
b)
In[4]:=
1 Cos Sin
Cos2 Sin2
Simpl
University of Calgary
Fall semester 2013
PHYS 615: Advanced Quantum Mechanics I
Homework assignment 6
Due Friday December 06, 2013
Problem 6.1. Verify numerically the Landau-Zener formula pD = e2 for the probability of a
(
)
2
=
diabatic transition, w