Quantum Foundations and Quantum Information: Problems Week 2
SCA
QF & QI 2014
Questions on physics
Problem 2.1: Double Slit Experiment, General Questions
In the double slit experiment how would the pa
QF & QI: Postulates of QM.
1
W4.3b
State
[1] McIntyre: Postulate 1) The state, including all you can know about it, is represented mathematically by
a normalized ket | .
[2] Shankar, Postulate I: The
Some calculus exercises to keep you sharp
SOLUTIONS
1: Some Basic Derivatives
What are the following derivatives? for this problem you may enter your answers on this sheet. (These are the
key results
QFQI 2014
.
Quantum Mechanics: Problems Lecture 15
15.1 Density matrices
The quantum state of an object is represented in the most general manner through the density matrix, = | |.
The motivation for
Ch. 3 Solutions
Assignment Week 6
Ch 3: 12, 13, 14
Ch 4: 1,2,3,4
3.12 The eigenstates and eigenvalues of H are, by inspection:
1
0 , E2
E = E1 , E2 ; E1
0
1
We need to find the eigenvectors of
Ch. 5 Solutions
Ch 5: 4,6,7,8,16,20,22,24,27,33
5.4 Assume the real solutions
E ( x ) = Asin kx + B cos kx
The boundary conditions yield
E ( a ) :Asin ka + B cos ka = 0 B cos ka = Asin ka
E ( a ) :
Ch. 2 Solutions
2.4 The general matrix is
a b
A
c d
The matrix elements are
+ A+ =
(1
a b 1
=
0
c d 0
(1
a
=a
0
c
+ A =
(1
a b 0
=
0
c d 1
(1
b
=b
0
d
A+ =
(
a b 1
=
0 1
EPGY P055
Light and Heat
Some calculus exercises to keep you sharp
1: Some Basic Derivatives
What are the following derivatives?
1.
dex
dx
2.
dex
dx
3.
d2 ex
dx2
=
4.
de
dx
=
5.
d2 eix
dx2
6.
d cos x
Ch. 1 Solutions
1.1. a)
1 = 3 + + 4
To normalize, introduce an overall complex multiplicative factor and solve for this factor
by imposing the normalization condition:
1 = C (3 + + 4
)
= cfw_C ( 3
Lecture 6B: Dirac formalism of Quantum Mechanics
Bra and ket vectors.
The following appendices are to provide a quick overview of some areas of mathematics that you may not
have been exposed to. The o
Summer College Academy
Quantum Foundations and Quantum Information
Postulate I: Quantum States
This section combines the rst chapter of Baym and the rst chapter of Scarani. Begin weigh the classical n
QF & QI: State vector
Administrative, technical issues.
Questions?
Classical polarization of light.
Quantum model of polarization.
Mathematical structure of states.
Born probability rule.
Bases
Summer College Academy 2014
Q.F & Q.I.
Lecture 12B: Existence of Joint Probability Distributions -signicance
The basic notions of probability have been reviewed before and here it will be assumed you
QF & QI: State vectors: Polarization
Administrative, technical issues.
Questions?
Fun with polarizers.
State vectors for polarization
Bases
W3.2
QF & QI: State vectors: Polarization
W3.2
Obtainin
10
Quantum Mechanics Lecture 11c Addendum: Mathematical details
Basic Experiments with Polarizers
We can verify the properties of the wavefunction and operators for a photon in some polarization state
QF & QI: State vectors: Polarization, details
Administrative, technical issues.
Questions?
Solution to previous days question
A little about circular polarization
Bases, transferring between.
Su