Deep Introduction to Quantum mechanics.ppt

introduction to quantum mechanics

1. January 8, 2013Course Content & the beginning
Raghava Varma
Department of Physics
Phone 7582, 4548
EP-307
Introduction to Quantum
Mechanics

2. January 8, 2013Course Content & the beginning
Reference Texts
Principles of Quantum Mechanics
R Shanker
Modern Quantum Mechanics
J.J. Sakurai

3. Course Content & the beginning
Method of Assessment
Two quizzes of 10 marks each
Internal Assessment 10 marks
Midsemester examination 30 marks
End Semester 40 marks
January 8, 2013

4. January 8, 2013Course Content & the beginning
Tone of the course
How and why?
The merging of two different disciplines
Linear Algebra
Physical world
Course on modern logic
Enjoy the course–Let it be like Movie,
Music, Swimming ---Whatever you like

5. Developments in the Last
Century
Defined by Physics
From pinnacle of wonder to depths of despair
Began with certainty of absolute knowledge
Ended with knowledge of absolute uncertainty
Built weapons that had the capacity to destroy this reality
Developed theory deny the possibility of ever
comprehending the nature of physical reality
January 8, 2013Course Content & the beginning

6. What was “The Theory”
Almost everything we think we know about the nature of our world
Most successful theory of physics ever devised
Concepts underpin much of the twenty first century technology
Completely undermined our ability to make sense of the world at the
level of its most fundamental constituents
For a person familiar with logic of Classical Physics
–Mathematically Challenging
–Maddeningly bizarre
–Breathtakingly beautiful
January 8, 2013Course Content & the beginning

7. The Theory (contd…)
In 112 years physicists have failed to get to grips and
understand what it means
Nobody understands how Quantum Theory actually works
The rules of its application are unquestioned
The accuracy and precision of its predictions unsurpassed
Albeit heated debates on its interpretation continue
No discussion on the correctness of the theory
January 8, 2013Course Content & the beginning

8. The Logical Tightrope
Evidence based investigations meeting scientific standards of
rigour should reveal true mechanism of nature
When quantum mechanical, however, world of science and
philosophy were set on a collision course
Instead of truth and comprehension we got deeply unsettling
questions about what we can we ever hope to know about the
nature
Quantum theory pushed us to edge of epistemological precipice
Mid 1920s we have lived in fear of slipping over the edge
January 8, 2013Course Content & the beginning

9. The theory took birth in 1900 in the porcelain furnaces used to
study black body radiation
It is looking forward to a new era, a new beginning with the
technological marvel, the Large Hadron Collider producing data
Long journey of hundred odd years there have been certain
defining moments.
Some of which you have already encountered in your Modern
Physics course
Some you will encounter in this course
Hopefully some more before you leave the portals of this Institute
January 8, 2013Course Content & the beginning

10. The Defining Moments we will Encounter
Planck’s quantum of action
Einstein’s light quantum hypothesis
Bohr’s quantum theory of atom
Louis de Broglie’s hypothesis
Heisenberg’s Matrix Mechanics
Pauli’s exclusion Principle
Schrödinger's wave mechanics
January 8, 2013Course Content & the beginning

11. Copenhagen Interpretation of Quantum Theory
The intense debate between Bohr, Heisenberg and Schrödinger on the
reality of quantum jumps
Max Born interpreting the significance of wave function
The development of the Uncertainty Principle
Einstein turning into a “non believer”Debates between Einstein &
Bohr
Einstein Podolsky Rosen argument, Schrödinger's cat
Dirac’s quantum theory of electron
The Defining Moments
January 8, 2013Course Content & the beginning

12. The jewel of physics QED
Unheralded development of Quantum Field Theories based on local
gauge symmetry
“Heavy Photons”Electroweak unification
Culminated in Gellman's theory of quarks
Introduction of symmetry breaking & the Higg’s Mechanism
History of quantum theory became synonymous with particle
physics
The Defining Moments after the war
January 8, 2013Course Content & the beginning

13. Larger and more expensive accelerators
Coupled with state of the art detectors
Physicists started inventing technology too!
Particle collection of Quantum Field theoriesThe
Standard Model of Particle Physics
Proton has structure at SLAC
Discovery of Charm J/Ψ at SLAC and BNL
W & Z at CERN
The Era of Experiments
January 8, 2013Course Content & the beginning

14. Never know the Truth
David Bohm’s uneasiness with Copenhagen Interpretation
Hidden variables alternative to conventional Quantum Theory
Experiments designed to probe the nature of physical reality
Bell’s theorem and Bell’s inequality
Quantum World shown to be determinedly non local
January 8, 2013Course Content & the beginning

15. The Grey areas
Experiments that strongly suggest that particle properties
we measure are not necessarily the properties of the
particles as they really are
We can never perceive reality
We can only reveal aspects of an empirical reality that
depend on the nature of the instruments
Quantum Physics has completed its transformation into
experimental philosophy
January 8, 2013Course Content & the beginning

16. The Frontiers
Finally effort to forge together two great physical theories of the twentieth
centuryQuantum Theory and General Relativity into Quantum Gravity or
alternately theory of everything
First Superstring revolution promised to provide a theory which could not only
explain all the particles of the SM but could also accommodate graviton
The early promise faded as a plethora of different variants of superstring
theory emerged
In 90’s the superstrings experienced something of a renaissance and dominate
contemporary Theoretical Physics
Impatience with string theories as fail to provide any testable predictions
Crisis once again is knocking the doors of Quantum theory
January 8, 2013Course Content & the beginning

17. Fortunate are you
Large Hadron Collider stands on the threshold of discovery
At worst will
–Confirm existence of Higgs
–Validate the mechanism of spontaneous symmetry breaking and the origin of mass
–Put the final icing on the cake of the standard model
At Best
–LHC will turn up some bizzare new experimental facts
–Facts beyond the quantum field theories that constitute the Standard Model
–The crisis will then deepen putting life into Physics
Only from the depths of despair are we likely to see the breakthru
needed to propel quantum theory into next stage of its journey
January 8, 2013Course Content & the beginning

18. January 8, 2013Course Content & the beginning
Contents of the course
Couple of Lectures on why Quantum
Mechanics?
And then just Shanker all the way
Mathematical Introduction
Linear Vector Spaces
Dirac Notation
Linear Operators
Active and Passive transformations
Eigenvalue problem
Genralization to Infinite Dimensions

19. January 8, 2013Course Content & the beginning
Contents of the Course (contd..)
The Postulates of Quantum Mechanics
The Postulates
Definition of the postulates
The Schroedinger’s Equation
QUIZ -I
Simple Problems in One Dimension
The free particle
The particle in a box
Continuity Equation for probability
Single Step Potential –a problem in scattering

20. January 8, 2013Course Content & the beginning
Contents of the Course (contd..)
The Classical Limit
Quantum mechanics often does not tend to classical
physics—
•when does it do?
•When it does not?
•Origin of Quantization
Simple Harmonic Oscillator
Why?
Quantization
Oscillator in energy basis
Generalization of postulate II
Gauge Invariance and choice of phase for wavefunction
QUIZ II

21. January 8, 2013Course Content & the beginning
Contents of the Course (contd..)
The Path Integral Formulation of Quantum
theory (May be)
The Path Integral Recipe
An approximate U(t) for free particle
Path Integral evaluation for free particle
Symmetries and their Consequences
Translational Invariance
Time Translational Invariance
Parity Invariance
Time-Reversal Invariance