Lecture 30
Review!
Announcements
Final Friday @ 11:30 York 2722
One Page Cheat Sheet! (front and
back)
bring blue book, calculator, pencil
Evenly cover all chapters
Finals Week Ofce Hours:
Bor-Yuan Tuesday 2-3 MH tutorial center
Me: Thurs 1-4pm Es
Review Part 1!
Chapters 1-4
Announcements
Final is June 15, Friday at 11:30 am
The location will be in York 2722
You are allowed a full page (front back) for a
cheat sheet.
Doodle Survey (posted online)
When would you like to have ofce hours during
n
Lecture 28
The Hydrogen Atom
Research Experience as an
Undergraduate
Students who do undergraduate research are more likely to go on to
graduate school, and on average become productive researchers in graduate
school faster. This is most true when undergr
Lecture 25
The Hydrogen Atom! For real!
Last Time
Math overload! (Quick Review?)
3D 3D in spherical coordinates!
r is the radius
is the
inclination
is the azimuth
Time Independent
Schrdinger
(r,t) = (r,)(t)
(r,) = R(r)()()
Last Time
Using the Coulom
Lecture 24
3D-QM
Last Time
Extended our 1-D model to 3-D
x
(r, t ) = (r ) ( t ) = (r )e it
Schrodingers eq:
Time independent
Schrodinger:
Particle in a 3D box
Particle in a 3D box
Solutions will be of the form:
~Asinkx+Bcoskx
Applying boundary
conditi
Lecture 23
Step Function, 3-D!
Last Time
I = Ae ikx + Be ikx
Quantum Tunneling
III = Fe ikx
The Step Potential
I
II
A free particle with E<U incident upon the potential step
Region I (U=0) Free particle wavefunction moving to
the right, with reected
Lecture 22
Quantum Tunneling
Last Time
Expectation Values:
Position:
(Average position)
< x >=
x ( x, t)
2
dx
Momentum:
(Average momentum) < p >=
using the momentum operator:
[ p] =
i x
* i x dx
sandwiching the operator in
between the square
Lecture 21
Expectation Values, Operators,
Uncertainty
Last Time
Quantum Oscillator
When a particle is acted on by a spring-like force where
F=-kx representative of a stable equilibrium
U=1/2Kx2 and =(K/m)
U(x)=(1/2)m2x2
TISE becomes:
E=(1/2)
Last
Lecture 20
The Quantum Oscillator and
Expectation Values
Quiz 3 results posted!
average = 8.7
100
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80
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Series1
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Announcements: No class Friday Sun God!
Quiz 4 is not till June 1st, covering chapter 6 and 7
Use t
Lecture 19
QM in 1-D: Finite Square Well,
Quantum Oscillator,
Expectation Values
Last Time
Particle in a box (Innite Well Problem)
(x)=0
=Asinkx+Bcoskx
(x)=0
Finding a Wavefunction
Guidelines:
1. Determine the form of the potential(s) in your
system
2.
Lecture 18
QM in 1-D: Particle in a box &
Finite Square Well
From Last Time
Can pick up quizzes at Discussion Section and
Problem Session if you did not get it last time.
Wave function, (x,t)
All possible information about a particle is contained in it
Lecture 17
QM in 1-D
Quiz 2 Results!
Average = 6.59
25
20
15
Series1
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0
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3
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7
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Last Time
Heisenberg Uncertainty Principle:
px x /2
E t /2
The precision with which we can know the
energy of some system is limited by the
time available
Lecture 16
Matter Waves, Heisenberg
Uncertainty Principle
Announcements
Quiz #3 in one week!
Covers chapters 4 and 5
Class Cancelled May 14th
Last Time
Goal: Describe a particle as a
pulse or a wave group
Review of traveling waves
Review of wave add
Lecture 15
More Matter Waves!
Last Time
De Broglies PhD thesis:
Matter has wave-like properties
Matter has a pilot-wave that steers it through
space and time
Electron-Wave Experiments
The Davisson-Germer Experiment 1927
Electron-Wave Experiments
Doub
Lecture 14
Matter Waves
Last Time
Bohrs Atom
Ephoton = hf = E = Ei-Ef
ke2/(2hca0) = R = 1.09737x107m-1
Last Time
Success of Bohrs Model?
Extremely successful in deriving all of the hydrogen
spectral lines for both emission and absorption
Problems:
Fai
Lecture 13
Bohrs Atom
Last Time
Rutherfords Experiment
Bohrs Postulates:
Postulates:
Electrons in atoms are generally conned to
certain stable, nonradiating orbits with discrete
energy levels - Stationary States
Under the inuence of the coulomb attra
Lecture 12
Millikans Oil Drop Experiment,
Rutherfords Experiment
Last Time
Experiments to determine the nature
of matter
Faradays Electrolysis Experiment
Atoms consist of positively charged stuf and
negatively charged stuf
Thomsons Cathode Ray Tube
E
Lecture 11
Particle Matter
Announcements
Quiz #2 this Friday!
blue book
index card cheat sheet
calculator
quiz code number
If you have lost or forgotten your number,
contact me or TA
Covers chapters 2 and 3!
Last Time
Compton Scattering
The expe
Lecture 10
Compton Scattering, WaveParticle Duality!
Quiz 1 Grades Posted!
Average: 7.01 out of 10
Graded tests will be distributed @ discussion today.
number of students
60
50
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30
20
10
0
1
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4
5
score
6
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8
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10
Last Time
Plancks blackbody radia
Lecture 9
Blackbody Radiation,
Photoelectric Efect
Last Time
General Relativity
Blackbody problem-
Why do glowing solids exhibit standard spectra that are only a
function of temperature?
Blackbody- an object that absorbs all incoming radiation
Blackb
Lecture 8
GR, Light
Last Time
Mass-Energy conservation
Fusion reactions
in sun:
Proton-Proton
chain
Last Time
Mass-Energy conservation
Inelastic collisions
M = 2 m
since is always >1
M is always >2m !
Two big new concepts:
Space-time
Mass energy
Ge
Lecture 7
Relativistic Mechanics &
General Relativity
From Last Time
Relativistic Momentum
Applying to newtons 2nd law
d
= (mu)
dt
F = ma(1 u 2 / c 2 ) 3 / 2
Applied work-energy thrm to derive KE
Dene rest mass ER=mc2
Total Energy E=mc2 = K + ER
Fi
Lecture 6
Relativistic Kinematics
Announcements
Special Thursday ofce hour @
Espresso Roma, 10:30 am- 12pm
Quiz Friday Covering Chapter 1 only
Bring a blue book.
Your quiz code # will be assigned on
Friday
Chapter 1 Solutions are posted.
From Last Ti
Lecture 5
Lorentz Transformations and
Spacetime intervals
Last time
Length Contraction
Relativistic Doppler Shift
Relativistic Doppler Shift
obs =
1 (v / c )
source
1 + (v / c )
What does this mean?
when relative velocity, v, is positive, wavelength
Lecture 4
More Consequences of Special
Relativity
For Next Time
Finish reading chapter 1
HW Chap 1: 5,8,12,13,14,16,
Relativistic Als adventure (Interactive link
online)
Quiz week Thursday ofce hour time?
Survey
From Last Time
Consequences of SR pos
Lecture 3
Consequences of Special
Relativity
From Last Time
Inertial Reference Frame a reference frame that is not
accelerating
Galilean Transformations- relate observations in two diferent
reference frames
try exercise 1
Note on terminology: Covariant
Lecture 2
Special Relativity Part 1
Announcements
Problem Session:
Thursday 8:00 P 09:50 PM PCYNH 109 (Pepper Canyon Hall)
Handouts and Links on course website:
http:/physics.ucsd.edu/students/courses/spring2012/
physics2d/coursehandouts.html
Physics
PHYS 2D
PROBLEM SESSION
2012/5/31
8.1
Particle in box with side L1=L, L2=L3=2L. Find 6
lowest energy & degeneracy
222
2
222
2
E1=n1 /2mL , E2=n2 /2m(2L) ,
E3=n3222/2m(2L)2
E=E1+E2+E3
22
2
E(1,1,1)=(1+1/4+1/4)=1.5 in unit of /2mL
E(1,1,2)=(1+1/4+1)=2.2
PHYS 2D
DISCUSSION SECTION
2012/5/30
Quiz this Friday
QM in 3D (math really)
More Realistic QM
Our world is 3 dimensional
Must use 3 coordinates
Study 2 cases:
Particle in a 3D box
-Essentially the same thing
Hydrogen atom
-Spherical coordinates, very