Assignment 9:Special Relativity"
Due Monday 14th May
!
1. A particle moves uniformly in frame S with velocity u, making an angle
with the xaxis. If is the angle with the xaxis in the usual second
frame S, prove the particle aberration formula:!
tan =
s
Assignment 8: Special Relativity
Due Monday 7th May
1.
Show that U2 = c2
2. Show that the 4velocity and the 4acceleration are orthogonal
(1 mark)
(2 marks)
3. Use the fact that the 4velocity transforms as a vector to rederive the
(6 marks)
velo
Assignment 7: Quantum Mechanics
Due Tuesday 1st May
1. Using the spin rotation formalism from lecture 16, construct a state
S n,
such that
S n S n, = / 2 S n,
where n is characterised by the angles shown in the gure. Express your
answer as a linear
Assignment 6: Quantum Mechanics
Due Tuesday 24th April
1. The propagator for a free particle is:
i m ( x x )2
i m
G( x, t; x , t ) =
exp
2 (t t )
2 (t t )
a) Show that if a propagator satises the Schrdinger equation, then a
wavefunction evolved wit
Assignment 5: Quantum Mechanics
Due Monday 26th March
1. If we make a unitary transformation such that the states and operators
transform using the same unitary operator:
U
Q U Q U
U U = UU = 1
a) Show that inner products between arbitrary states are
Assignment 4: Quantum Mechanics
Due Monday 19th March
1. Prove the Schwarz inequality for vector spaces:
Hint: Let =
2
and use
0
2. Prove that for a complete orthonormal basis
cfw_ j ,
(3 marks)
j
j
j
is the identity.
(4 marks)
Assignment 3: Classical Mechanics
Due Tuesday 13th March
1. A particle slides on the frictionless surface of the interior of a
45cone.
a) Find the 2D Lagrangian in terms of the
vertical coordinate z and an angular
coordinate .
(4 marks)
b) Find the H
Assignment 2: Classical Mechanics"
Due Monday 5th March
!
!1. Consider a pendulum free to swing without friction at a pivot,
with a second pendulum attached to it with its pivot at the centre of
mass of the rst pendulum. These are not simple pendula, so t
Assignment 1: Classical Mechanics
Due Monday 27th February
Light paths during a mirage
1. The velocity of light above a hot surface decreases with the height
from that surface. The velocity is given by
0.5
1.0
1.5
2.0
 0.05
y
v = v 0 1
 0.10
 0
Do you dont you want me to make you / Im coming down fast but Im miles above you
Tell me, tell me, tell me the answer: You may be
Theoretical Physics
but you aint no dancer
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Housekeeping
Second Project
Poli
Art is long, and time is
Theoretical Physics
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
We learned to write physical
relationships using tensors
E =
Maxwells equation:
J = c , j x , j y , j z
(
)
= 0 J
unchanged for all choices of gauge
Would it have been worthwhile if
Theoretical Physics,
settling a pillow, or throwing off a shawl / And turning to the window should say:
That is not it at all / That is not what I meant at all
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Secon
Stand up against governments, against
Theoretical Physics.
Stay irresponsible. / Say only what we know & imagine
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Second Project
Draft due tomorrow. Attach to Wattle post.
Feedback in Wattle thr
I am putting myself to"
Special Relativity"
Housekeeping
!
which is all I think any conscious entity can ever hope to do
!
Second Project!
Joe Hope
!
X52780, room 103
!
joseph.hope@anu.edu.au
!
Draft due this Friday (at midnight)!
Feedback due next Wedn
What if I told you
Special Relativity
is only a special case of General Relativity, but writing physics with tensors is universal?
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Review: 4vectors
All 4vectors transform according to the Lorent
(Im)
Special Relativity
(Ill marry you in a ash / Im whos on rst / Im Big Bird / Im hers, yeah. Im hers.)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Housekeeping
Second Project
Post your project title on Wattle
Post your intention to r
In loyalty to their kind, they cannot tolerate our
Special Relativity
In loyalty to our kind, we cannot tolerate their obstruction!
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Review: 4vectors
All 4vectors transform according to the Loren
(And as in the dark all cats are grey, the Pleasure of)
Special Relativity
(is at least equal, and frequently superior,
every Knack being by Practice capable of improvement)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Review: Relativity
On
(Were ye at the place / Cad
Special Relativity?
(Saw ye Geordies grace / Riding on a goosie?)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Review: Postulates of relativity
1. Physics (results of experiments) is invariant between all
inertial
Special Relativity
(minor, standard)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
GPS IIR15
Review: Postulates of relativity
1. Physics (results of experiments) is invariant between all
inertial frames.
2. Light propagates in a vacuum iso
(Phys3001, your work is unparalleled.
And Im a huge fan of how you lose control and turn into)
Special Relativity
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Feedback on Project 1
First, it is clear that many people found this project hard
Quantum Mechanics
Andre Carvalho
61970038, room 110
andre.carvalho@anu.edu.au
Approximate Methods
Review: Variational Methods
Provides upper bounds for the ground state energy:
Remember: it works for any
.
So start by choosing a good trial fu
Quantum Mechanics
Andre Carvalho
61970038, room 110
andre.carvalho@anu.edu.au
Approximate Methods
Review: Variational Methods
Provides upper bounds for the ground state energy:
Remember: it works for any
.
So start by choosing a good trial fu
Quantum Mechanics
Andre Carvalho
61970038, room 110
andre.carvalho@anu.edu.au
Approximate Methods
Review: Variational Methods
Provides upper bounds for the ground state energy:
Perturbation Theory
H = H0 + V
Time independent: eigenvalues and
Quantum Mechanics
Andre Carvalho
61970038, room 110
andre.carvalho@anu.edu.au
Approximate Methods
1. Only few problems in QM can be solved exactly.
2. Approximate methods are necessary to deal with many important
problems in QM:



Variation
Quantum Mechanics
(formed again, and yet again, as endless aeons wheeled and passed.)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
Path Integral Formulation
A classical object has a position and a momentum. By
contrast, in QM, it is in a supe
(Thats life, she said, We should be dead. We should be
Quantum Mechanics
( and perfect tens. And thats just three off the top of my head.)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
There is no quantum world. There is only an abstract physic
(Slide your hand / Jump off the end / The)
Quantum Mechanics
(is clear / and innocent)
Joe Hope
X52780, room 103
joseph.hope@anu.edu.au
No assignment this week to give extra time to nish projects
Anyone who is not shocked by quantum theory has no
(Now, since what were proposing here is so unusual, so outside the norm, that this is a good bet
that this will be one of those incidents that sticks. So, since youre gonna be stuck remembering)
Quantum Mechanics
(for the rest of your life, you have to de