Physics 424: Quantum Mechanics, Fall 2015
Reading/Homework Assignment 7
Due in Class Wednesday, 11/4/15
1
Reading
•
(Optional: Townsend Sec. 5.6 – Entanglement and Quantum Telepor
tation.
Will not be covered in class or on tests but you might find
interesting.)
•
Townsend Sec. 5.7 – The Density Operator
•
Townsend Sec. 5.8 – Summary
•
Townsend Sec. 6.1 – Position Eigenstates and the Wave Function
•
Townsend Sec. 6.2 – The Translation Operator
•
Townsend Sec. 6.3 – The Generator of Translations
You don’t need the following section for these HW problems, but we will
start discussing these topics in class:
•
Townsend Sec. 6.4 – The Momentum Operator in the Position Basis
Problems to work out and turn in (70 pts total)
1. (10 pts) Show the following result, which we used in our discussion of
Bells inequality:
C
ab
=
4
¯
h
2
h
0
,
0

ˆ
S
a
1
ˆ
S
b
2

0
,
0
i
=

cos
θ
ab
.
Here

0
,
0
i
is the singlet state of two spin1/2 particles,
ˆ
S
a
1
is the oper
ator for the component of spin 1 in the
a
direction,
ˆ
S
b
2
is the operator
for the component of spin 2 in the
b
direction, and
θ
ab
is the angle
between the
a
and
b
directions.
Hint: Since the

0
,
0
i
state has no preferred direction, you are free (for
example) to take the
a
direction to be
z
, and to take the
You've reached the end of your free preview.
Want to read all 3 pages?
 Fall '15
 mechanics, Work, pts, Townsend, Canonical Ensemble, Townsend Sec.