BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
Instruction Division
Second Semester 2014-2015
Course Handout
Date: 12/01/2015
Course Number
Course Title
: PHY F315
: THEORY OF RELATIVITY
Instructor-in-Charge
: TAPOMOY GUHA SARKAR
Scope &
Half-page derivation of the Thomas precession
Andrzej Dragan1 and Tomasz Odrzyg
ozdz2
arXiv:1211.1854v1 [physics.class-ph] 8 Nov 2012
1
Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-049 Warsaw, Poland
2
College of Inter-Faculty Indiv
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The Overcoat
Once upon a time in a town called St. Petersburg, there was a low-ranking officially who
was unfortunately named Akaky Akakievich Bashmachkin. Akaky was a poor guy, but he
loved his job. In fact, he loved it so much that all he did when he we
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI (RAJ)
FIRST SEMESTER 2015-2016
Linear Vector Space
ASSIGNMENT 2
1
Linear vector space
A vector space V over C (set of complex numbers) or R (set of real numbers) is a set of objects denoted by
| and labele
FORCED OSCILLATIONS
In this experiment, the arc used in the electromagnetic
induction experiment serves as the oscillator, it is driven
by a motor, with the help of a string spring combination,
whose rotational speed can be controlled. When required
a dam
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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:
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