PH 107
Quantum Physics
B.N. Jagatap
jagatap@phy.iitb.ac.in
Extn.: 9377
A warm
welcome to IIT
Bombay
and to the
course on
Quantum
Physics
Remember to Have Fun on
Your First Day and Relax!
We shall have a great
semester!!
About this course
PH 107
Quantum Physics
Quantum Theory is the theoretical basis
of modern physics that explains the
nature and behaviour of matter and
energy at atomic and sub-atomic level.
Also called as Modern Physics
How Modern?
Not really so modern!
Seeds were planted more than a century ago….
Why do I learn Quantum Physics?
Not true for Quantum Physics!
Why do I learn Quantum Physics?
Every student and practitioner of
science and engineering needs it
You cannot afford to ignore it.
If you understand it well, you can
participate in the science and technology
endeavours of 21st century.
Electrical & Electronics
Engineering
Semiconductor devices
Nanoelectronics: Nanometer sized quantum
tunnelling devices
Spintronics: Devices based on electron spin
Photonics: Devices based on photons
Quantum tunnelling is how
flash drives erase their
memory
Giant magnetoresistance is
what allows hard disk
drives to function
AlGaAs Quantum wells are what
allow lasers and photonics
AlGaAs
“In this paper, I examine connections between
electrical engineering and quantum physics research
in Japan. Japan was one of the first countries that have
successfully developed quantum physics research
relatively early outside Europe and North America.
I claim that electric engineering was one of the bases
for quantum physical research to be motivated,
legitimized and sustained.”
Computer Sciences
& Engineering
Quantum Computer &
Quantum Information
Processing
Cool Quantum Tech: This dilution
refrigerator can cool quantum dots to
less than 5 millikelvins for
experiments in quantum computing.
Material Engineering,
Chemical Engineering
Novel materials, graphene,
topological insulators
Molecular and thermodynamic properties
based on molecular structure that have large
potential for optimization and design of
processes
Combustion, ignition, lubricants, fuel injection, design
of solvents, drugs etc.
Caltech: Department of Mechanical and
Civil Engineering
Quantum Mechanics at the Macroscopic Scale:
Coarse-graining Density Functional Theory
Multiscale
Modelling
What has Architecture to do with Quantum
Physics: About Buildings and Systems
“Building is part of a dynamical system. Although
those systems that matter to a building can be
described reasonably accurately with classical
Newtonian knowledge, to understand the bigger
context and its systems, a less ‘mechanical’
knowledge is required. Quantum Mechanics,
phase transitions, tipping points and emergence
could indeed help us to be useful in solving even
more complex problems and dynamical issues”
Neri Oxman
Europe Will Spend €1 Billion to Turn
Quantum Physics Into Quantum
Technology
A 10-year-long megaproject will go beyond
quantum computing and cryptography to
advance other emerging technologies
By Alexander Hellemans
Posted 22 Jun 2016 | 15:00 GMT
“Many areas of quantum mechanics are no longer
problems of physics; they are now engineering
problems.”
Even the financial markets need knowledge of
Quantum Physics!
This Course
Covers developments leading to birth of
Quantum Physics
Provides a flavour of Quantum Physics and
its applications (to Solid State Physics)
Gives some insight into how well
established theories in physics gave way to
newer theories
Classical Physics
All phenomena can be described either as a
particle or a wave.
Position and momentum of any particle are
exactly determined at any given time.
Waves exhibit phenomena that can not be
explained in a classical particle; Interference
and Diffraction
Accessible energies are continuous.
Position and momentum of any particle are
’objective’ properties whether or not their
values are known explicitly to physicists.
If values of position and momentum were not
known, but were needed for further
calculations, one would make reasonable
(statistical) assumption about them. e.g.,
Maxwellian velocity distribution
If we exactly duplicate all conditions of
experiment, the outcome must turn out to be
exactly same: Doctrine of ‘determinism’
Quantum Physics is bizarre
Particles can behave as waves and waves can
behave as particles: Wave Particle Duality
Energy can not be divided into arbitrary small
parts, instead there is a smallest undividable
energy package called a ‘quantum’, e.g., E=h
Quantum system can adopt specific values of
energies, whereas others are forbidden: Energy
Quantization
Position and momentum of a particle cannot
be determined to arbitrary precision, but are
determined by uncertainty relation.
Uncertainty relation brings in fuzziness which
blurs the classical quantities: Probabilistic
description
Wave function:(x,t) a state vector that
contains all information of the particle.
Classical Physics
Warning:
Our intuition, rooted
in daily experience
Quantum Physics
with classical world
utterly fails to
visualize the complex
wave function (x,t).
Quantum mechanical equations were
postulated to explain experimental
observations, but the deeper meaning of the
equations often confused the most gifted.
‘God does not play with dice’
Einstein
“I think I can safely say that nobody
understands quantum mechanics”
Richard Feynman
You need some knowledge of maths: Perform
integration, Deal with differential equations……
All these we shall learn during this course.
Topics to be discussed:
Introduction to quantum ideas: Physics towards the end
of nineteenth century and emergence of new experimental
results, concept of degrees of freedom, equipartition of energy,
specific heat of mono-atomic, di-atomics, solids, black body
radiation, Planck’s quantum hypothesis and black body
radiation law, Einstein’s model for specific heat of solids, photo
electric effect and Einstein’s theory, brief concepts of relativity,
Compton effect, line spectra and Bohr’s atomic model.
De Broglie wave and Heisenberg uncertainty relation:
Wave properties of electrons, Davisson-Germer experiment,
electron microscope, electron interference experiment, wave
packets, phase and group velocity, dispersion relations, Fourier
transform, Heisenberg uncertainty relation, examples of
uncertainty relation.
Shrodinger equation: Wave function, operators,
Hamiltonian, probability, normalization, averages,
superpositions, Time dependent and independent Shrodinger
equation in one dimension.
Bound state problems: Solution of Shrodinger equation
for various types of 1-d boxes, symmetry of wave functions,
comparison between classical and quantum particles in box,
quantum harmonic oscillator, comparison with classical
oscillator. Copenhagen interpretation, wave function collapse.
Free state problems: Scattering and tunnelling, probability
current, reflected and transmitted wave, penetration in the
classically forbidden region, square barrier, reflection and
transmission coefficient, tunnelling, transmission resonance,
scanning tunnelling microscope and alpha decay.
Quantum mechanics in 3-d: Shrodinger equations in 3-d,
free particle, particle in 3-d box, 3-d harmonic oscillator,
concept of degeneracy.
Introduction of quantum statistics: Distinguishable and
indistinguishable particles, macro and micro states, Maxwell
Boltzman distribution (energy and speed), mean, mean
square/most probable speed/energy, Bosons and Fermions,
symmetric and antisymmetric wave function, Bose-Einstein
and Fermi-Dirac statistics, concept of density of states and
Fermi energy.
Applications of BE and FD statistics: Black body
radiation law, free electron theory of metals, contribution of
conduction electrons to heat capacity of solids at low
temperatures, Bose-Einstein condensation.
Drude and Drude Sommerfeld Models: Drude’s
models for electric conduction, heat conduction and hall
effect. Drude-Sommerfeld model, Fermi
surface/momentum.
Band theory of solids: Kronig-Penny model, electrons in
crystalline solid, periodic boundary condition, Bloch
theorem, effective mass, allowed bands and forbidden gaps,
dispersion relation.
Reference Books
Modern Physics by Serway, Moses and Moyer
3rd Edition
Indian edition available
PDF version available
on internet
Modern Physics : K.S. Krane; John Wiley
1998, 2nd Edition
Introduction to Modern Physics :
F.K. Ritchmyer, E.H. Kennard, John N. Cooper;
Tata McGraw Hill, 1976, 6th Edition
Concepts of Modern Physics: Arthur Beiser,
McGraw Hill, 1987, 4th Edition
Quantum Physics: R. Eisberg and R. Resnik,
John Wiley, 2002, 2nd Edition
Moodle
Lecture slides will be uploaded on Moodle
within a week (Very next day in all
probability)
These slides are for personal use of the
students registered in this course only.
Lecture slides cannot be put on any other
server, shared on the internet or mailed to
anyone not registered for this course
Good to Remember
> One hour class 14.00-15.25 Hrs (Tue) and
14.00-15.25 Hrs (Fri) every week
Tutorials will start soon (will let you know).
The first tutorial will contain some problems
which are expected to be known to you.
It will be presumed that any announcement
made in the class will reach everyone. No
additional notice may be circulated.
Evaluation Scheme
In-semester (60%)
Quiz-1 in August (15%), Quiz-2 in October (15%)
Mid-sem in September (30%)
End-semester in November (40%)
All quizzes/exams are compulsory. No re-exam
or compensation in any form will be given on
any ground whatsoever.
There will be a quiz question in every tutorial,
which will be considered for the final
evaluation of marks.
Attendance Policy
80% attendance is mandatory
Each lecture will be developed based on the
ideas developed in the previous lecture(s)
Attendance is helpful in understanding the
subject
Students with poor attendance find it
difficult to cope with tests and often land up
with poor grades or ……………..
Have Fun on
Your First Day
and Relax!
and continue
having it (at
least) all over
this semester!
Good
Luck
Recapitulate
Classical Physics
Physics before 20th century, i.e., physics before the
birth of Quantum Mechanics
Mechanics
Electrodynamics
Thermodynamics
Mechanics
Newton’s first law:
Law of inertia
Newton’s second law: F ma
Introduces force ( F ) as responsible for the
change in linear momentum ( p m v ) F d p / dt
Newton’s third law: F21 F12
Law of action and reaction
m1m2
Newton’s law of gravitation: F G 2 r
r
Electrodynamics Maxwell’s Equations
Gauss’s law (Electric field) E / 0
Relationship between electric field and the
electric charges that cause it
Gauss’s law (Magnetic field) B 0
No magnetic monopoles
Faraday’s law E B / t
Time varying magnetic field creates electric filed
Ampere’s law B 0 0 E / t
Time varying electric field to magnetic field
1 2
E
Wave equation E 2 2
2
c t
Light is an electromagnetic wave with velocity 1
c
0 0
Thermodynamics
Zeroth Law: This is the game
Two systems in thermal equilibrium with a third system are in
thermal equilibrium with each other.
First Law: You cannot win
You cannot get something out of nothing, because matter and
energy are conserved. U=Q+W
Second Law: You cannot break even
Any transfer of energy will result in some wastage (disorder)
unless temperature of absolute zero is achieved.
Stotal = Ssurrounding +Ssystem
Third Law: You cannot get out of the game
Absolute zero is unattainable.
Thinking of Physicists towards the end of 19th century
“The more important fundamental laws and the facts
of physical science have all been discovered and they
are so firmly established that the possibility of their
ever being supplanted in consequence of the new
discoveries is exceedingly remote…. Our future
discoveries must be looked for in sixth place of
decimal”
Michelson (1899)
But there were problems looking for satisfactory
answers………
Black body radiation
Specific heats of gases and solids
Line spectra of atomic gases
Photoelectric effect
Cathode rays and X Rays
Compton effect
