Physics 228
Exam results:
Today: Lorentz Transformations
Doppler Effect
Review: Lorentz Transformation
x' = (x u t)
y' = y
y = y'
z = z'
z' = z
t' = (t u
x = (x + u t')
x/c2)
t = (t + u x'/c2)
world line of Mavis
Mavis moving at
u = 0.6 c
(lines of simult

Microscopic Theories of Conduction
1
10
Localized states
8
6
4
Energy
2
Extended states
0
-2
-4
-6
-8
-10
0
5
15
20
10
Disorder width W
26th August 2003
c 2003, Michael Marder
Denitions
2
Weak Scattering Theory
Noise
MetalInsulator Transitions
Green

Phonons
1
Time
Acoustic
Optical
Space
14th April 2003
c 2003, Michael Marder
Denitions
2
Phonons
Goldstone modes
Acoustic branch
Optical branch
Density of phonon states
Einstein model
Debye model, Debye frequency, Debye temperature
Gr neisen param

Optical Properties: Phenomenological Theory
1
21st September 2003
c 2003, Michael Marder
Optical Properties: Phenomenological Theory
2
soft X-ray
ultraviolet
infrared
red
green
blue
microwave
105
1018
Core-level
photoemission
Plasma frequency
p in metals

Dynamics of Bloch Electrons
1
7th September 2003
c 2003, Michael Marder
Denitions
2
Drude model
Semiclassical dynamics
Bloch oscillations
K P method
Effective mass
Houston states
Zener tunneling
Wave packets
Anomalous velocity
WannierStark ladde

Electronics
1
26th August 2003
c 2003, Michael Marder
Denitions
2
Work Functions
Schottky Barrier
Intrinsic Semiconductors
Doping
Semiconductor Junctions
Rectication
Diodes and Transitors
Heterostructures
Two-Dimensional Electron Gas (2DEG)
Quan

Optical Properties of Insulators
F3 or R center
1
VK center
(A)
(B)
21st September 2003
c 2003, Michael Marder
Denitions
2
Polarization
Optical Modes
Polaritons
Polarons
Point Defects
Color Centers
Electron Spin Resonance
FranckCondon Effect
Urba

Optical Properties of Metals
1
Germanium
10
8
6
2
(eV)
15
4
25
0
2
nk
Energy
-2
-4
-6
-8
-10
-12
1
-14
L
X
Wave vector k
21st September 2003
c 2003, Michael Marder
Denitions
2
Phenomenology of Metals
Anomalous Skin Effect
Plasmons
Interband Transition

Quantum Mechanics of Interacting Magnetic
1
Moments
100
FC
AFC
AF
AF
AF
U
10
F
F
G
Coppersmith
P
1
kaxiras
Richter
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
100
Sarker
F
Davila
Schumacher
F
S
U
10
P
1
AF FC
F
IC
AF
P
FI
0.0 0

Classical Theories of Magnets
A
1
13
1.00
n nc
1
0.90
0.70
O2
Kr
T Tc
A
0.80
N2
CO
CH4
1
1.0
1.5
n nc
2.0
2.5
3.0
(B)
0.5
0.50
0.0
2
1
A n nc
0.60
Xe
Ne
28th September 2003
c 2003, Michael Marder
Denitions
2
Phenomenology of Magnets
Dipole Moments
Ferr

Superconductivity
(B)
1
5000 A
25th October 2003
c 2003, Michael Marder
Denitions
2
Perfect Diamagnetism
LandauGinzburg Equations
Type I and Type II Superconductors
Flux Quantization
Josephson Effect
Superconducting Quantum Interference Devices (SQU

Magnetism of Ions and Electrons
1
Scaled magnetic induction b
1.0
0.5
0.0
0
1
3
2
Energy
4
28th September 2003
c 2003, Michael Marder
Denitions
2
Atomic Magnetism
Hunds Rules
Curies Law
Landau Diamagnetism
AharonovBohm Effect
Hofstadter Buttery
Int

Fluid Mechanics
1
1st May 2003
c 2003, Michael Marder
f
(L4)
r
(L6)
r
r
r
(L7)
P
!
r
t
r
t
t
P
t
(L5)
P
0
t
t
(L3)
0
P
(L2)
t
(L1)
f r t dt
rt
dt
dt t
r
2
Eulers Equation
1st May 2003
c 2003, Michael Marder
Eulers Equation
3
P
(L8)
(L9)

Transport and Fermi Liquids
gx
gx
dx
A
x
dx
x
x
x
a
Are
1
dx
26th August 2003
c 2003, Michael Marder
Denitions
2
Boltzmann Equation
Relaxation Time Approximation
Onsager Relations
Holes
WiedemannFranz Law
Seebeck, Peltier, and Thomson Effects
Class

Cohesion of Solids
1
31st March 2003
c 2003, Michael Marder
Cohesion of Solids
2
Solids divide into 5 rough classes for purposes of studying cohesion
Molecular
Ionic
Covalent
Metallic
Hydrogen bonded
Goal is to obtain conceptual and semi-quantitative

Physics 228 Today:
Relativity:
Force, Energy, Momentum
Photoelectric Effect:
Photons, Work Function
Momentum and Force
Momentum p = mv, in special relativity becomes p = mv.
Newtons second law applies to this relativistic momentum:
For a force in the dire

Physics 228
Today: Special Relativity: Continued
Principle of Relativity: Physical laws, including speed of light,
are the same in every inertial reference frame.
Results in:
relativity of simultaneity
time dilation
length contraction
twin paradox
Transve

Condensed Matter Physics
1
Largest subeld of physics
Link between atoms and everyday world.
Unity obscured by tremendous variety of topics.
16th May 2003
c 2003, Michael Marder
Dividing the eld
Historical Roots
2
Concepts
Atomic Structure
Selforganiz

Physics 228
Today:
Nuclear Physics
Radioactivity
Stability of Nuclei
Here we plot the lifetime of
the nuclei (color, black is
stable) in a chart of neutron
number N (y-axis) vs. proton
number Z (x-axis).
There is a narrow valley of
stability around an opt

Physics 228
Today:
Light-Emitting and Laser Diodes
Solar Cells
Transistors
Atomic Nuclei
Review: p-n Junction Diode
Charge transfers across the junction until the Fermi levels on both sides
are the same. This results in
Two opposite space charge regions

Physics 228
Today:
Free Electron Metals
Semiconductors
p-n Junction Diode
iClicker
The difference between an ionic and a covalent bond is
a.
Ionic bonds are only found in crystals such as NaCl
where there are many atoms in close proximity.
b.
Covalent bon

Problem of conductivity: Drude model
m is the relaxation time. t
0e t
1
eE
m
(L1)
(L2)
Steady state, times much longer than :
e E m
(L3)
Current therefore is j ne ne2 E m
is the electrical conductivity ne2 m
(L4) (L5)
9th February 2003

The Single-Electron Model
1
l
Pl2 2Ml
1 2
l l
ql ql Rl Rl
(L1)
18th May 2003
c 2003, Michael Marder
Approximations
l
2
Pl2 2Ml
1 2
l l
ql ql Rl Rl
Nuclei treated as classical potentials. Many electrons combined with nuclei in closed shells

Born-Oppenheimer approximation
N
N
(L1)
l l
l 1
rl
l 1
rl
Uion rl
2
l
e2
h2
2m
1
the underlying physical laws necessary for the mathematical theory of a large part of
physics and the whole of chemistry are thus completely known, and the difculty is only

ThreeDimensional Crystals
1
16th May 2003
c 2003, Michael Marder
Topics
2
Distribution of structures among elements
A small number of popular crystal structures
Crystal symmetries:
7 crystal systems
14 Bravais lattices
32 point groups
230 space gro

Band Structure Calculations
1
8
6
Energy (eV)
4
2
0
-2
-4
-6
-8
P
N
H
Wave vector k
23rd March 2003
c 2003, Michael Marder
Pseudopotentials
2
Question: How could it ever be true that electrons in a metal think they are moving freely
in an empty box?
Pseud

Elasticity
1
10th April 2003
c 2003, Michael Marder
General Theory of Linear Elasticity
Before deformation
2
After deformation
u r2
r2
u r1
r1
ur
r
r
(L1)
Many ways to derive elasticity. Could derive from theory of atoms and their interactions.
However, t

Instructions for 2012 tour of the Lawrence Berkeley National Laboratory:
The tour will last from 10:00 am until about 4:00 pm, and will include a lecture and videos on the
Laboratory overall, as well as tours of the Advanced Light Source and the National