PHYS 17 (IQMSM)
Review Sheet for Midterm 2
Winter 2014
The Exam
The exam will take place on 28 February 2014 at 11am.
As I understand it you are allowed one page of notes. Other than that, you are not allowed ANY outside
materials. Do not bring books, not
Discussion Plan: Week 1
For PHYS 17, 8 Jan 2013
Erin Hansen
Albert Brown
1
ehansen@physics.ucla.edu
albertnbrown@ucla.edu
Housekeeping:
Discussion is held on Wednesdays at 3pm in PAB 2434. Clubhouse oce hours are held on
Wednesdays 4-6pm in Knudsen 2-222.
15
Quantum mechanics in three dimensions
If anybody says he can think about quantum physics without getting giddy, that only shows he has
not understood the rst thing about them. Niels Bohr
15.1
Schrdinger equation
o
Now that we have established the found
11
Foundations of quantum mechanics
Like an ultimate fact without any cause, the individual outcome of a measurement is, however, in
general not comprehended by laws. This must necessarily be the case. Wolfgang Pauli
11.1
Wavefunction
Particles behave as
12
Innite square well and simple harmonic oscillator.
dependence of the wavefunction.
Time-
The career of a young theoretical physicist consists of treating the harmonic oscillator in everincreasing levels of abstraction. Sidney Coleman
12.1
Innite square
13
Examples
Problem 45 An electron (me = 0.511M eV /c2 ) is inside a box of width 300nm, in state n = 3.
What are all the possible frequencies of radiation when the electron transitions to a lower state (3
to 2 followed by 2 to 1 is also a possibility)? N
9
Particles as waves
After long reection in solitude and meditation, I suddenly had the idea, during the year 1923,
that the discovery made by Einstein in 1905 should be generalised by extending it to all material
particles and notably to electrons. Louis
10
Heisenberg uncertainty principle
The solution of the diculty is that the two mental pictures which experiment lead us to form the one of the particles, the other of the waves - are both incomplete and have only the validity of
analogies which are accur
7
Quantization of light
All the fty years of conscious brooding have brought me no closer to answer the question, What
are light quanta? Of course today every rascal thinks he knows the answer, but he is deluding
himself. Albert Einstein
7.1
Blackbody rad
8
Models of the atom
If, in some cataclysm, all scientic knowledge were to be destroyed, and only one sentence passed
on to the next generation of creatures, what statement would contain the most information in the
fewest words? I believe it is the atomic
6
Examples
Problem 23 A spaceship of proper length 200m is moving with speed 0.5c with respect to the earth.
A light pulse is sent from the back end of the spaceship to the front end, which gets reected by a
mirror and comes back (see below). How long doe
17
Spin and Pauli exclusion principle, the periodic table
The fundamental laws necessary for the mathematical treatment of a large part of physics and the
whole of chemistry are thus completely known, and the diculty lies only in the fact that application
18
Examples
Problem 60 An electron (me = 0.511M eV /c2 ) is in 1-dimensional potential
U (x) =
ax4
4
where a = 1eV /nm4 . Using the uncertainty principle estimate the ground state energy of the
electron.
Problem 61 The radial wavefunction for a particle i
14
Step potential and quantum tunneling
Scientic knowledge is a body of statements of varying degrees of certainty some most unsure,
some nearly sure, none absolutely certain. Richard Feynman
14.1
Step potential
The next system that we discuss quantum mec
Photon Statistics 1
A single photon in the state r has energy r = r.
The number of photons in any state r may vary from 0 to .
The total energy of blackbody radiation is ER = r nrr , where
nr is the number of photons in the rth state, so that
Zph(T, V)
Fundamental Theorems of Vector Calculus
GREENS THEOREM(S)
FUNDAMENTAL THEOREM OF LINE INTEGRALS
(
)
(
)
IF THERE EXISTS A SCALAR POTENTIAL FUNCTION (
)
FOR F, THEN THE LINE INTEGRAL OF THE VECTOR FIELD F
DEPENDS ONLY ON THE BOUNDARIES OF THE CURVE!
From t
The Minkowski Spacetime Diagram1
Events happen. They are not bound to and, in fact, happen in spite of,
any frame of reference we may or may not choose to describe them in. The
Minkowski spacetime diagram gives us a way to overlay events with multiple
fra
Transformations1
In the simplest terms, Special Relativity is all about transforming the description
of events observed in one inertial frame of reference into valid descriptions in
some other inertial frame of reference.
Geometric Transformation
y
P
y
x
Magic1
Time Dilation
S
Suppose a beacon is mounted on the nose of the rocket. If it ashes regularly
with a temporal interval t , the coordinates that describe two consecutive
ashes in the rocket frame would look like:
r1 =
ct1
x1
r2 =
c(t1 + t )
x1
and th
Relativistic Dynamics1
The Scalar Product in Euclidean 3-Space
The scalar product in Euclidean 3-space is dened by:
A B |A|B | cos
where is the angle between A and B . Equivalently,
A B = Ax Bx + Ay By + Az Bz
Its reasonably easy to show that
AB A B
that
Applied Relativistic Dynamics1
As we work our way through the following examples, there are a few things
youll want to keep in mind:
The inner-product
Ei Ej
Pi P j
cc
produces a value that is the same in all inertial frames of reference.
Pi Pj
The 4-m
Some Important Examples1
Compton Scattering
f
i
According to classical theory, when an electromagnetic wave scatters o an electron, its wavelength remains unchanged - this is in direct contradiction with the
experimental observation that wavelength increa
16
The hydrogen atom
The mathematical framework of quantum theory has passed countless successful tests and is now
universally accepted as a consistent and accurate description of all atomic phenomena. Erwin
Schrdinger
o
16.1
Energy levels and radial wave
4
Relativistic momentum and energy
We are trying to prove ourselves wrong as quickly as possible, because only in that way can we
nd progress. Richard Feynman
4.1
Relativistic momentum
Newtons second law is invariant under Galilean transformations, howeve
5
Energy vs. mass, introduction to general relativity
If I had only known, I would have been a locksmith. Albert Einstein
5.1
Energy and mass
As we discussed earlier, objects even at rest possess energy, proportional to their mass
Erest = mc2
and in every
Solutions for Midterm #2
PHYS 17 - Winter 2014
Problem 1
An atom can radiate at any time after it is excited. It is found that in a typical case
the average excited atom has a life-time of about 10 8 seconds. That is, during period
it emits a photon and i
Introductory Notes on Probability Theory
Grigor Aslanyan
October 28, 2009
1
Denition of probabilities
Let us imagine a class of 100 physics students that have to take a physics test. Each student
wants to know her overall standing among everybody else, so
PHYS212-071
HW # 8 (Chapter 6) Solutions
(Numbers refer to 2nd Edition of Textbook)
1. A particle incident on the potential step of Example 6.5 with a certain energy E < U is
described by the wave
1
( x) = (1 + i ) e ikx + (1 i ) e ikx For x 0
2
( x ) =
Homework Problem Set No. 8 Due Wednesday, December 3, in class 1. Calculate the equilibrium temperature of the Earth. Assume that the Sun radiates 3.9 1026 watts, that the albedo of the Earth is 0.3 and that the Earth is 1.5 1011 m from the Sun. 2. Assume