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Prasanta Kumar Das

Professor

Astrophysics and Cosmology, High Energy Particle Physics
D 320/18 New Academic Building, BITS Pilani K K Birla Goa Campus

Teaching

Semester I, 2025-26: List of student project problems will be uploaded soon. Interested students can fill the google form (to be made available here). He/she needs to attach his/her one page CV(that should contain the list of course that he/she has completed/registered till now, his/her programming efficiency, CGPA, etc.)  in the form. 

In this semester (Semester II, 2024-25), I am teaching the following two courses: (i) Particle Physics and (ii) General Theory of Relativity(GTR) and Cosmology.

A. Particle Physics (PHY F413)
 
Course description

This course aims to introduce the basic concepts of  Particle Physics. The main objective is to know how the fundamental particles (e.g. electron, muon, quarks, photon, gluon etc) interact with each other at high energy. After reviewing basic concepts of special relativity (in 4 vector formalism), non- relativistic and relativistic quantum mechanics, the free-particle relativistic wave equations i.e. Klein-Gordan equation (spin-0 particle - pion), Dirac equation(spin-1/2 particle - electron), Maxwell equation(spin-1 article - photon) will be derived. The role of symmetry and conservation laws in Particle Physics will be discussed at a length. A brief overview of group(Lie) theory will be given.  The gauge theory of electron-photon interaction(Quantum Electrodynamics(QED)) will be developed and a brief introduction of electron-proton(e-p) deep-inelastic scattering will be given. Few  QED processes e.g. the muon pair production in electron-positron annihilation, Bhabha scattering, and decay of neutral Z and Higgs(H) boson  will be discussed at a length. 

Books:

TB1: Modern Particle Physics, Mark Thomson, Cambridge University Press(2013).

Reference Books:
RB1: Introduction to Elementary Particles, D Griffiths, Wiley VCH.
 
Students' project:
  1. Dark Matter relic density calculation using microOmega
  2. On some aspects of non-Abelian gauge theory.
  3. Scattering cross-section of Compton scattering.
 
To the students -
  • For the class schedule, evaluation components, make-up policy, please refer the course handout which are available in your respective  LMS quanta page.
 
B. General Theory of Relativity & Cosmology (PHY F415)
 
Course description

This course aims to introduce the basic concepts of  General Theory of Relativity and it's application in Cosmology i.e. to know the behavior of the universe at large scale. After reviewing basic concepts of special relativity (in 4 vector formalism), the notion of tensor, covariant derivative, geodesics, curvature tensor, Ricci tensor, Ricci scalar, Einstein tensor and hence the Einstein  equations will be derived. The Schwarzschild black hole solution of the Einstein equation will be discussed, which will be followed by Physics near the massive objects. The FRW cosmology will be discussed at a length and finally inflationary cosmology will be introduced in brief.

Text Books:

TB1: A short course in General Theory of Relativity, Foster and Nightingale (Springer).

Reference Books:
RB1: S. Weinberg, Gravitation and Cosmology, John Wiley, New York, (1972).
RB2: M. Rowan-Robinson, Cosmology, 3rd edition, Oxford University Press (1996).
RB3: J. A. Peacock: Cosmological Physics, Cambridge University Press (1999).
RB2: Modern Cosmology, Scott Dodelson, Academic Press (2006).
 
Students' project:
  1. Inflationary cosmology
  2. Solving Einstein equations using the GRTTensor
  3. Active Galactic nuclei(AGN) processes
To the students -
  • For the class schedule, evaluation components, make-up policy, please refer the course handout which are available in your respective  LMS quanta page.
Earlier semester(s):

  • In Semester I, 2024-25, I have taught two courses: Quantum Mechanics for Engineers (a UG course) and Quantum Theory & Applications(a PhD level course)
  • In Semester II, 2023-24, I have taught the course Electromagnetic Theory II.
  • In Semester I, 2023-24, I have taught the course Electromagnetic Theory I.
  • In Semester II, 2022-23,  I have taught  (i) Astronomy and Astrophysics and (ii) Mechanics, Oscillations and Waves. 
  • In Semester I, 2022-23,  I have taught  (i) Statistical Physics & Applications(a PhD level course) and (ii) Particle Physics
  • In Semester II, 2021-22,  I have taught (i) Quantum Mechanics I and (ii) General Theory of Relativity and Cosmology. 
  • In Semester I, 2021-22, I have taught (i) Quantum Physics and Application(a PhD level course) and (ii) Statistical Mechanics. 
  • In Semester II, 2020-21, I have taught (i) Theory of Relativity and (ii) Cosmology. 
  • In Semester I, 2020-21, I have taught (i) Particle Physics and (ii) GTR and Cosmology.

The set of courses that I taught in BITS: I have taught the following courses(CDC, Elective, Multi-section): (i)Mechanics, Oscillations & Waves, (ii) Electrodynamics, (iii) Classical Mechanics, (iv)Quantum Mechanics I & II, (v) Modern Physics, (vi)Statistical Mechanics, (vii)Mathematics III (Differential Equations and it's application), (vii) Nuclear & Particle Physics, (viii) Theory of Relativity, (ix)Particle Physics, (x) Introduction to Astronomy & Astrophysics, (xi)General Theory of Relativity & Cosmology, (xii) Physics Laboratory I, (Xiii) Advanced Physics Lab.

On top of this several students did their SOP, CP and LOP under my supervision over several years.

===============

Semester I, 2024-25:

A. Quantum Mechanics I (PHY F242) 
 
Course description
This course will provide the basic grounding in Quantum Mechanics for the undergraduate students.  Topics to be covered in this course are (i) Fundamental concept (Hilbert space, Bra, Ket vectors, Operators, uncertainty relations, Wave functions), (ii) Quantum Dynamics (Time evolution of wave function, the  Schrodinger vs Heisenberg picture, SHO), (iii) Angular Momemtum (Rotations and angular momentum commutations relation, spin 1/2 system, eigen values and eigenstates of angular momentum, orbital angular momemtum, angular  momentum addition), (iv) Symmetry in quantum mechanics (symmetries, conservation laws and degeneracies, discrete symmetries etc), (v) Time-Independent perturbation theory, non-degenerate and degenerate cases, Stark effect and Zeeman effect. (vi) Variational principle and its application.

Text Books:

TB1:  Introduction to Quantum Mechanics, D. J. Griffith, 2nd Edition, Pearson Education.

Reference Books:
 
RB1: Modern Quantum Mechanics, J. J. Sakurai, Pearson Education, Twelfth Impression, 2013.
RB2: Quantum Physics, S. Gasiorowicz, Wiley 1974. 
 

Student corner:

Few interesting videos - 

1.  Can machine think? R. Feynman (click)
2.  Knowing versus understanding. R. feynman (click
3.  Secret of Concentration. Swami Sarvapriyananda (click
4.  Positive psychology. Seligman (click)  
5.  Secret of happiness. Mihaly Csikszentmihalyi  (click
 
List of SOP/LOP/CP project problems:
 
Students interested in doing SOP, CP or LOP can send his/her one page CV to me at pdas@goa.bits-pilani.ac.in. See below the list of problems that you may work on.  
 
Specific Project problems: 
1. Machine Learning and Neutron star Equation of State
2. Deep learning for gravitational wave forecasting of neutron star mergers
3. Bose-Einstein condensation through machine learning
4. Machine Learning for the solution of Schrodinger Equation
5. Convolutional Neural Network and direct detection of dark matter
6. Dark Matter and Galaxy Rotation curve - A ML approach.
7. Machine Learning Applied to the Reionization History of the Universe in the 21 cm Signal
8. Quantum Potential prediction using Deep Neural Network
9. A ML approach in Stock-market prediction
10. The role of Artificial Intelligence(AI) in High Energy Physics, Astro(particle)physics and Cosmology (open problem)
 

Broad areas of Student's projects -    Astronomy & Astrophysics, Cosmology & High Energy Physics
1. The cradle of life: Astro-biology
2. Extraterrestrial Intelligence
3. Cosmology expansion rate measurement
4. Nature of Dark Matter
5. Cosmology(acceleration) with Dark Energy
6. Gravitational lensing
7. Gravitational wave in Astronomy
8. Hydrogen-I science in cosmology
9. Re-ionization problem
10. Transient universe
11. Supernovae and its remnants
12. Pulsar science
13. Angular momentum in cosmology
14. Galaxy formation and Dark Matter 
15. Radio-Astronomy
16. The world as viewed by HST
17. The role of AI in the search of New Physics
 
Computer  Projects
1. GEAS(General Education Astronomy Source) project
 
UG Thesis problems: 
 
High Energy Physics:
After the discovery of Higgs particle (also known as GOD particle) at Large Hadron Collider@CERN on 4th July,2012, the next question now people are asking: what's next? Is there anything beyond the Standard Model of Particle Physics? Is there any kind of New Physics. If yes, how it looks like and how to probe this. Can one test these ideas in high energy colliders e.g. proton-proton Large Hadron Collider, electron-positron Linear Collider?
 
Problem:  Searching for New Physics signatures at high energy electron - positron linear collider. 
Prerequisites: Understanding of Special Relativity, Quantum Mechanics and familiarity with the basics of Particle Physics. 
 
Astrophysics: 
In 1987 the core collapse supernova (SN1987A) was observed in a nearby galaxy called the Large Magellanic Cloud. The total energy emitted in SN1987A explosion was larger than that by 10 billion Suns. The kinetic energy of the explosion carries about 1% of the gravitational binding energy of about  ergs and the remaining 99% going into neutrinos.
Now the numerical neutrino light curves can be compared with the SN1987A data where the measured energies are found to be “too low”.It is remain unclear whether this anomaly is due to a statistical problem or whether there is some New Physics.  

Problem: Constraining new physics from supernova, relic density constraint 
Prerequisites: Special Relativity, Quantum Mechanics, Particle Physics. Some familiarity  with Quantum Field Theory may be useful. 
  •  To know more about my research work and my group, click here.
 

Semester 2, 2021-2022
  • Students who are interested to work on project problems in Semester 2, 2021-22, are requested to fill the google form (click here) on or before 20th November 2021. 
  • List of students selected for Project type course- Semester II, 2021-22 (click here)  (NEW)
 
Semester 1, 2021-2022
 
NEW: List of students who may work under my supervision in Semester 1, 2021-22 after getting registered into project  type courses is available here