3.4 Physics Major Courses
PHY301: Classical mechanics


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Course Outline

Lagrangian
formulation
of
mechanics.
Degrees
of
freedom
and
equations
of
motion.
Constraints
and
Generalized
coordinates.
Principle
of
least
action.
Emphasis
on
the
Variational
principle.
The
Calculus
of
Variations.
EulerLagrange
equations.
Constrained
systems
and
Lagrange
multipliers.

Phase
space
formulation.
Hamiltonian,
phase
space,
Poisson
brackets.
Canonical
transformations.
Liouville’s
theorem
and
Poincare
recurrence.
HamiltonJacobi
theory.
Actionangle
variables.

Oscillators.
Small
fluctuations.
Damped,forced
and
anharmonic.
Eigenvalue
equation
and
principle
axis
transformation,
normal
coordinates,
forced
oscillations
and
resonance,
vibrations
of
molecules.
Nonlinear
oscillations
and
chaos.

Motion
in
a
central
field.
Equivalent
onebody
problem.
first
integrals,
classification
of
orbits,
virial
theorem,
Bertrand’s
theorem
Kepler’s
law.
Symmetries
and
conservations
laws.
Noether’s
theorem.
Central
forces
in
three
dimensions.
Scattering
in
a
central
force
field,
Rutherford
scattering.

Rigid
bodies.
Rotation.
Orthogonal
transformations,
Euler
angles,
rigid
body
dynamics,
spinning
top.
Recommended Reading

H. Goldstein,
C. P. Poole
and
J. L. Safko,
Classical
mechanics,
03rd
edition,
AddisonWesley
(2001).

L.
D.
Landau
and
E.
M.
Lifshitz,
Mechanics,
03rd
edition,
Butterworth
Heinemann
(1976).

N.
C.
Rana
and
P.
S.
Joag,
Classical
Mechanics,
Tata
McGrawHill
(1992).

V.
I.
Arnold,
V.
V.
Kozlov
and
A.
I.
Neishtadt,
Mathematical
aspects
of
classical
and
celestial
mechanics,
03rd
edition,
Springer
(2006).

J. V. Jose
and
E. J. Saletan,
Classical
dynamics:
a
contemporary
approach,
Cambridge
University
Press
(1998).

W. Greiner,
Classical
Mechanics

Systems
of
Particles
and
Hamiltonian
Dynamics,
Springer
(2002).
PHY302: Quantum mechanics


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Course Outline

Classical
vs.
quantum
Mechanics,
Simple
2state
QM
system.
Hilbert
Spaces,
Operators.
Observables

Compatible
Observables,
Tensor
Product
Spaces,
Uncertainty
Relations.
Position,
Momentum
and
Translation.
Eigenvalue
Problems.
Emphasis
on
Linear
Vector
Spaces
from
a
mathematical
point
of
view.

Time
Evolution
(Quantum
Dynamics).
Schroedinger,
Heisenberg
and
Interaction
Pictures;
Energytime
Uncertainty,
Interpretation
of
Wavefunction.
Quantum
Particles
in
Potential.
Harmonic
oscillator.

Angular
Momentum.
Rotation
in
Quantum
mechanics.
SO(3)
vs.
SU(2).
Spherical
Harmonics.
Addition
of
Angular
Momenta.

Single
electron
atoms: Spherically
symmetric
potentials,
spherical
harmonics,
Hydrogen
atom
problem,
solution
of
Schroedinger
equation,
energy
levels
and
eigenfunctions,
orbital
angular
momentum,
Hydrogenic
atoms.
Recommended Reading

L. I. Schiff,
Quantum
mechanics,
03rd
edition,
McGrawHill
Publishers
(1968).

J. J. Sakurai,
Modern
quantum
mechanics,
AddisonWesley
(1993).

C. CohenTannoudji,
Quantum
mechanics
Vols
1
and
2,
WileyInterscience
(2006).

J.
D.
Bjorken
and
S.
D.
Drell,
Relativistic
quantum
mechanics,
McGrawHill
(1998).

R.
Shankar,
Principles
of
quantum
mechanics,
02nd
edition,
Springer
(1994).

W.
Greiner
and
B.
Muller,
Quantum
mechanics

Symmetries,
02nd
edition,
Springer
(2004).
PHY303: Electrodynamics


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Course Outline

Electrostatics.
Boundary
value
problems.
Method
of
images.
Green’s
functions.
Eigenfunction
expansions.
Series
solution
of
PDE.
Laplace
equation
in
spherical
and
cylindrical
coordinates.
Special
functions.
Legendre
polynomials,
Associated
Legendre
functions
and
Spherical
harmonics,
Bessel
functions.
Multipole
expansion.
Electric
fields
in
dielectrics.
Boundary
value
problems
in
dielectrics.

Magnetostatics.
Biot
and
Savart
Law.
Ampere’s
law
vector
potential.
Magnetic
field
in
matter.
Boundary
conditions.
B
and
H
fields.
Magnetization.
Faraday’s
law.
Energy
in
the
magnetic
field.

Electrodynamics.
Maxwell
equations.
Displacement
current.
Scalar
and
vector
potentials.
Gauge
transformations.
Electromagnetic
waves.
Pointing
vector.
Electromagnetic
waves
in
media.

Relativistic
formulation
of
electromagnetism.
F^{μ,ν}
and
its
transformation
properties.

Dipole
radiation.
Fields
or
moving
charges.
Retarded
potentials.
Recommended Reading

J. D. Jackson,
Classical
Electrodynamics,
03rd
edition,
Wiley
NY
(1998).

D. J. Griffiths,
Introduction
to
Electrodynamics,
03rd
edition,
PrenticeHall
NJ
(1999).

L. D. Landau
and
E. M. Lifshitz,
The
Classical
theory
of
fields,
04th
edition,
Pergamon
Press
(1994).

W.
K.
H.
Panofsky
and
M.
Phillips,
Classical
electricity
and
magnetism,
02nd
edition,
Dover
Publications
(2005).

J. Schwinger,
L. L. DeRaad
Jr.,
K. A. Milton,
and
WY. Tsai,
Classical
Electrodynamics,
Perseus
Book
Group
Massachusetts
(1998).

W.
Greiner
and
J.
Reinhardt,
Quantum
electrodynamics,
04th
edition,
Springer
(2008).
PHY304: Statistical mechanics


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Course Outline

Review
of
thermodynamics: Laws,
processes,
thermodynamic
stability.

Review
of
probability:
one
random
variable,
probability
distributions,
random
walks,
many
random
variables,
central
limit
theorem,
information,
entropy
and
estimation.

Kinetic
Theory
of
gases:
Liouville’s
theorem,
Boltzmann
transport
equation.

Classical
statistical
mechanics: Microcanonical,
canonical,
and
grand
canonical
ensembles.

Quantum
statistical
mechanics: Identical
particles,
Quantum
microstates
and
macrostates,
BoseEinstein
and
FermiDirac
statistics,
quantum
ideal
gases,
example
systems.

Phase
transitions: Cumulant
expansion,
van
der
Waals
equation,
variational
methods,
corresponding
states,
phase
transitions,
critical
point
behaviour.
Recommended Reading

K. Huang,
Statistical
Mechanics,
02nd
edition,
Wiley
(1987).

F. Reif,
Fundamentals
of
Statistical
and
Thermal
Physics,
McGrawHill
International
(1987).

L. D. Landau
&
E. M. Lifshitz,
Statistical
Physics,
03rd
edition,
ButterworthHeinemann
(1980).

Mehran
Kardar,
Statistical
Physics
of
particles,
Cambridge
University
Press
(2007).

W.
Greiner,
L.
Neise,
H.
Stocker,
and
D.
Rischke,
Thermodynamics
and
Statistical
Mechanics,
Springer
(2001).

S.K. Ma,
Statistical
Mechanics,
World
Scientific
(1985).
PHY306: Advanced quantum mechanics


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Course Outline

Time
independent
and
time
dependent
perturbation
theory.
Transitions
under
the
action
of
a
perturbation
acting
for
a
finite
time,
Transitions
under
the
action
of
a
periodic
perturbation.

Review
of
Hydrogen
atom,
Fine
structure,
Hyperfine
structure
as
an
application
of
perturbation
theory
to
real
systems.
Zeeman
effect,
Stark
effect.

The
semiclassical
approach,
WKB
approaximation.
Penetration
through
a
potential
barrier.

The
variational
principle,
applications.

Scattering
theory:
Scattering
crosssection,
partial
waves,
Yukawa
and
Coulomb
potentials,
scattering
by
square
well
potential,
reaction
rates,
mean
free
path,
retarded
potentials,
Born
approximation.

Relativistic
quantum
mechanics:
KleinGordon
equation,
negative
probabilities.
Dirac
equation,
relativistic
free
particle
solutions,
negative
energy
solutions,
antiparticles.
Zitterbewegung.
Recommended Reading

B. H. Bransden
and
C. J. Joachain,
Physics
of
Atoms
and
Molecules,
02nd
edition,
Pearson
Education
(2008).

P.
Atkins
and
J.
De
Paula,
Physical
Chemistry,
08th
edition,
Oxford
University
Press
(2009).

J. J. Sakurai,
Quantum
Mechanics,
Addison
Wesley
Low
Priced
Edition
(2008).

L. I. Schiff,
Quantum
Mechanics,
03rd
edition,
McGrawHill
(1968).

W. Demtroder,
Atoms,
Molecules
and
Photons,
SpringerVerlag
Berlin
(2006).

J. B. Rajam,
Atomic
Physics,
S.
Chand
&
Company
Ltd.
(2007).
PHY310: Mathematical methods for physicists I


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Course Outline

Complex
algebra:
Functions
of
complex
variables,
CauchyRiemann
conditions,
Cauchys
integral
theorem,
Laurent
expansion,
singularities,
mapping,
conformal
mapping.
Calculus
of
residues,
Dispersion
relations,
method
of
steepest
descent.

Gamma
and
Beta
functions:
Gamma
function,
definition
and
properties,
Stirlings
series,
Beta
function,
Incomplete
Gamma
function.

Differential
equations:
Partial
differential
equations,
First
order
differential
equations,
separation
of
variables,
singular
points,
series
solutions
with
Frobenius
method,
a
second
solution,
nonhomogenneous
equations,
Greens
function,
Heat
flow
and
diffusion
equations.

SturmLiouville
theory:
Self
adjoint
ordinary
differential
equations,
Hermitian
operators,
GramSchmidt
orthogonalization,
completeness
of
eigenfunctions,
Greens
function
eigenfunction
expansion.

Special
functions:
Bessel
functions
of
the
first
kind,
orthogonality,
Neumann
functions,
Hankels
functions,
Asymptotic
expansions,
Spherical
Bessel
functions.
Legendre
functions,
generating
function,
recurrence
relations,
orthogonality,
alternate
definitions,
associated
Legendre
functions,
spherical
harmonics,
Hermite
functions,
Laguerre
functions.
Recommended Reading

H.
J.
Weber
and
G.
B.
Arfken,
Essential
Mathematical
Methods
for
Physicists,
Academic
Press
(2004).

D.
A.
McQuarrie,
Mathematical
Methods
for
Scientists
and
Engineers,
Viva
Books
(2009).

Mary
L.
Boas,
Mathematical
Methods
in
the
Physical
Sciences,
Wiley
(2005).
PHY311: Advanced optics and spectroscopy lab


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Course Outline

Advanced
optics
experiments
involving
study
of
coherence
on
Michelson
interferometer
and
FabryPerot
atelon.

Spectroscopic
experiments
like
Zeeman
effect,
IR
spectroscopy
and
NMR
spectroscopy
will
be
used
to
study
atomic,
molecular
and
nuclear
spin
resonances.
PHY312: Advanced electronics and instrumentation lab


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Course Outline

Microcontroller:
Architecture
and
design.
Executing
electronic
circuits
using
the
microcontroller.
Logic
Gates,
Flip
Flops,
Registers
and
Counters.
Basic
digital
I/O.
DigitaltoAnalog
and
AnalogtoDigital
conversion.
Counting
and
Timing.
Timing
Diagrams.
Motor
Control
using
the
microcontroller.
Servo
motors
and
Stepper
Motors.

FPGA:
Introduction
to
FPGA
basic
architecture.
Programming
with
Verilog
and
VHDL.
Building
a
function
generator
using
FPGA
board.
Digital
logic
circuits.

Automation:
Data
acquisition
and
interfacing
with
PC.
Automation
of
physics
laboratory
experiments.
Programming
with
Phoenix.
Programming
with
LabView.

Student
Project:
Individual
project
to
be
conceived
and
executed
by
each
student,
in
any
of
the
three
areas
outlined
above.
Recommended Reading

C. Steiner,
The
8051/8052
microcontroller:
architecture,
assembly
language
and
hardware
interfacing,
Universal
(2005).

D. W. Preston
and
E. R. Dietz,
The
art
of
experimental
physics,
Wiley
(2009).

S. Ghoshal,
Embedded
systems
and
robots:projects
using
the
8051
microcontrollers,
Cengage
learning
Asia
(2009).

S. Brown
and
Z. Vranesic,
Fundamentals
of
digital
logic
with
VHDL
design,
McGraw
Hill
(2005).

C. Maxfield,
The
design
warrior’s
guide
to
FPGAs,
Elsevier
(2004).
PHY401: Nuclear and particle physics


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Course Outline

Basic
Ideas:
History.
Particle
exchange,
range
of
forces,
units:
length,
mass
and
energy,
review
of
special
relativity,
particle
decay.

Structure
of
Nuclei:
The
shell
model:
basic
ideas.
Spins,
parities
and
magnetic
moments
in
the
shell
model;
excited
states
in
the
shell
model.
Fermi
gas
model.
Collective
model.
βDecay.
Fermi
theory.

Nuclear
Phenomenology:
Notation;
mass,
spin
and
binding
energies.
Nuclear
forces;
shapes
and
sizes;
Liquid
drop
model:
semiempirical
mass
formula.
Nuclear
stability.
α,
β,
γ
decay.

Fission
and
Fusion:
Induced
fission
–
fissile
materials.
Fission
chain
reactions.
Power
from
nuclear
fission:
nuclear
reactors.
Nuclear
fusion:
Coulomb
barrier.
Stellar
fusion.
Fusion
reactors.

Experimental
Methods:
Overview,
accelerators,
beams,
particle
interactions
with
matter.
Particle
detectors
(measurement
of
position,
momentum,
particle
identification,
energy
measurements).

Review
of
Dirac
equation,
covariant
form
of
Dirac
equation,
relativity
and
antiparticles,
bilinear
covariants,
zero
mass
Fermions.

Elementary
particles:
Lepton
multiplets.
Lepton
numbers.
Neutrinos.
Neutrino
mixing
and
oscillations;
numbers
of
neutrinos.
Evidence
for
quarks;
properties
of
quarks;
hadrons.
Flavour
independence
and
hadron
multiplets.

Electroweak
Interactions:
Charged
and
neutral
currents.
Symmetries
of
the
weak
interaction.
Spin
structure
of
the
interactions.
Neutral
kaons.
K_{0}K_{0}
mixing
and
CP
violation.
Strangeness
oscillations.
W_{Ã±}
and
Z_{0}
bosons.
Weak
interactions
of
hadrons.
Neutral
currents
and
the
unified
theory.
The
Higgs
boson.
Recommended Reading

L.
D.
Landau
&
E.
M.
Lifshitz,
Quantum
Mechanics,
Volume
3
of
A
Course
of
Theoretical
Physics,
Pergamon
Press
(1965).

B.
Povh,
K.
Rith,
C.
Scholz
and
F.
Zetsche,
Particles
and
Nuclei:
An
introduction
to
the
physical
concepts,
Springer,
6th
edition
(2008).

B.
R.
Martin
and
G.
Shaw,
Particle
Physics,
03rd
edition,
Wiley
(2008).
PHY402: Solid state physics


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Course Outline

Periodic
Structure
and
Symmetry
of
Crystals.
Fundamental
types
of
lattices.
Simple
crystal
structures.
Diffraction,
Bragg’s
Law,
Reciprocal
Lattice.

Chemical
Bonding
(Ionic,
covalent,
hydrogen,
metallic).
Lattice
Dynamics,
Phonons.
Brioullin
zones.
Group
and
phase
velocity.
Thermal
Properties.
Normal
modes,
density
of
states,
Debye
theory,
Einstein
model.

Free
Electron
Gas
in
1D,
2D,
3D.
Heat
capacity.
Electrical
conductivity.
Hall
effect.
Thermal
conductivity.
Nearly
Free
Electron
Approximation.
Bloch
Theorem
and
Band
Structure.
KronigPenney
model.
Tight
Binding
Method.
Fermi
Surface.

Semiconductors:
Band
Gap,
Electrons,
Holes,
Impurities.
Band
theory
for
semiconductors.

Magnetic
properties
of
materials.
Concepts
of
Dia,
Para,
Ferro
and
Antiferro
Magnetism.
Introduction
to
Superconductivity
&
Superfluidity.
Recommended Reading

C. Kittel,
Introduction
to
Solid
State
Physics,
08th
edition,
John
Wiley
&
Sons,
Inc.
(2004).

N.
W.
Ashcroft
&
N.
D.
Mermin,
Solid
State
Physics,
Saunders
College
Publishing
(1996).

H.
Ibach
&
H.
Luth,
Solid
State
Physics,
Springer
(2003).
PHY403: Atomic and molecular physics


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Course Outline

Multielectron
atoms: Schroedinger
equation
for
He
atom,
spin
wavefunction
and
Pauli’s
exclusion
principle,
ground
state
and
first
excited
state,
complete
level
schemes
of
He,
Other
multielectron
atoms.
ThomasFermi
approach
and
HartreeFock
approximation
for
studying
multielectron
atoms.

Molecules:
Hydrogen
molecular
ion,
Hydrogen
molecule,
BornOppenheimer
approximation,
FrankCondon
transition,
molecular
potential
energy
curves,
Molecular
orbitals,
Morse
potential
formalism.

Spectroscopy
of
atoms
and
molecules:
Fine
and
Hyperfine
structure
of
atoms,
electronic,
vibrational
and
rotational
spectroscopy
of
molecules,
selection
rules,
some
experimental
techniques
of
spectroscopy.

Atom
Radiation
interactions:
Semiclassical
description
of
radiation.
Absorption,
spontaneous
and
stimulated
emissions,
Einstein’s
A
and
B
coefficients,
Coherent
and
Incoherent
emissions,
LASERs
and
MASERs,
Line
widths,
various
types
of
line
broadening,
twolevel
atoms
in
a
radiation
field.
Recommended Reading

B. H. Bransden
and
C. J. Joachain,
Physics
of
Atoms
and
Molecules,
02nd
edition,
Pearson
Education
(2008).

P.
Atkins
and
J.
De
Paula,
Physical
Chemistry,
08th
edition,
Oxford
University
Press
(2009).

J. J. Sakurai,
Quantum
Mechanics,
Addison
Wesley
Low
Priced
Edition
(2008).

L. I. Schiff,
Quantum
Mechanics,
03rd
edition,
McGrawHill
(1968).

W. Demtroder,
Atoms,
Molecules
and
Photons,
SpringerVerlag
Berlin
(2006).

J. B. Rajam,
Atomic
Physics,
S.
Chand
&
Company
Ltd.
(2007).
PHY411: Nuclear physics lab


[Cr:4,
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Tt:0,
Lb:9]
Course Outline

GeigerMuller
(GM)
Counter
based
experiments:
To
become
acquainted
with
the
operation
and
characteristics
of
the
GM
counter.
To
determine
the
best
operating
voltage
and
the
resolving
time
of
a
GM
counter.
To
determine
the
dead
time
of
the
GM
counter.
To
investigate
the
Binomial,
Poisson
and
Gaussian
probability
distributions
by
counting
radiation
events
with
a
GM
counter.
To
study
the
statistical
fluctuations
which
occur
in
the
disintegration
rate
of
an
essentially
constant
radioactive
source.
To
use
a
GM
detector
to
detect
the
gamma
ray
emitted
by
a
shortlived
excited
isotope
of
Barium.

Scintillation
counter
based
experiments:
To
study
the
scattering
of
highenergy
photons
by
electrons.
Detection
of
scattered
photons
in
a
scintillation
counter.
Measuring
energies
of
scattered
photons
and
recoil
electrons
as
function
of
scattering
angle.
Use
a
plastic
scintillator
as
a
target
and
record
relative
intensities
of
scattered
photons
at
several
scattering
angles.
Recommended Reading

G.
F.
Knoll,
Radiation
detection
and
measurement,
03rd
edition,
John
Wiley
and
Sons
(1999).

William
Leo,
Techniques
for
nuclear
and
particle
physics
experiments:A
howto
approach,
02nd
edition,
Springer
Verlag
(1994).

A.
Melissinos,
Experiments
in
modern
physics,
Academic
Press
(1966).
PHY412: Condensed matter physics lab


[Cr:4,
Lc:1,
Tt:0,
Lb:9]
Course Outline
In this course students will perform two kinds of experiments.

Measurements
on
various
materials
using
standard
equipment.

Hall
effect
to
study
carriers
in
semiconductors.

Fourprobe
method
for
resistance
measurement.

Magnetic
hysteresis
loop
on
various
magnetic
materials

Resistance
and
Magnetoresistance
of
some
standard
materials.

KCl
Fluorescence.
Study
and
color
centers.
 Advanced and nonstandard experiments

Meissner
effect
of
YBCo

Design
and
fabricate
a
dipstick
to
measure
resistance
versus
temperature
of
a
superconductor
(YBCo)
between
nitrogen
and
room
temperature.

Study
of
sand
piles.
Recommended Reading

C. Kittel,
Introduction
to
Solid
State
Physics,
08th
edition,
John
Wiley
&
Sons
Inc.
(2004).

M. Tinkham,
Introduction
to
Superconductivity,
02nd
edition,
Dover
Publications
(2004).