Teaching

Quantum Mechanics - II course in TIFR. Course largely devoted to angular momentum and approximation methods.

Recommended textbooks

(a) J J Sakurai, Modern Quantum Mechanics

(b) L I Schiff, Quantum Mechanics

(c) L D Landau and E M Lifshitz, Quantum Mechanics: non-relativistic theory

Lecture slides (2023)

1. Lecture 1 Linear superposition, states and observables

2. Lecture 2 Time evolution, density matrices

3. Lecture 3 Angular momentum (ladder operators, wavefunctions)

4. Lecture 4 Angular momentum (addition)

5. Lecture 5 Angular momentum (effect of rotations on states and operators)

6. Lecture 6 Angular momentum  (effect of rotations, Wigner-Eckart)

7. Lecture 7 WKB approximation (boundary conditions)

8. Lecture 8 WKB (bound states, tunnelling)

9. Lecture 9 WKB (tunnelling, transition probabilities, Landau-Zener-Schwinger mechanism)

10. Lecture 10 Variational principle

11. Lecture 11 Variational principle (eigenvalue interlacing theorem); Time-independent perturbation theory

12. Lecture 12 Perturbation theory (helium atom, anharmonic oscillator, quadratic Stark effect)

13. Lecture 13 Perturbation theory (degeneracies, linear Stark effect)

14. Lecture 14 Perturbation theory (linear Stark effect, spin-orbit interaction, relativistic correction to kinetic energy, Zeeman effects)

15. Lecture 15 Perturbation theory (Zeeman effects, Bloch theorem)

16. Lecture 16 Perturbation theory (hyperfine effects, time dependent perturbations - interaction picture)

17. Lecture 17 Time dependent perturbations (interaction picture, Dyson series, Fermi Golden Rule, state "decay", Breit-Wigner resonance)

18. Lecture 18 Time dependent perturbations (linear response, periodic perturbations, light absorption and stimulated emission, interaction of matter with classical EM fields) 

19. Lecture 19 Time dependent perturbations (light absorption by matter); Scattering theory (S and T matrice, Lippmann-Schwinger equation)

20. Lecture 20 Scattering theory (scattering amplitude, differential scattering cross-section, Born approximation)

21. Lecture 21 Scattering theory (spherically symmetric scattering potentials: partial waves and phase shifts, scattering length, low and high energy scattering)

22. Lecture 22 Scattering theory (forward scattering, optical theorem, resonant scattering)

A three-lecture set on basic concepts of superconductivity, presented at the Physics of Quantum Matter School in May 2023.

Recommended book

Michael Tinkham, Introduction to Superconductivity

Lecture slides

1. Lecture 1 Superconductivity: basic concepts (coherent state, Cooper instability, BCS superconductivity)

2. Lecture 2 Superconductivity: basic concepts (Bogoliubov quasiparticles, finite temperature effects, Josephson effect, dc SQUIDs)

3. Lecture 3 Superconductivity: basic concepts (Josephson arrays, phase fluctuations, Ginzburg-Landau theory)

Mini-course at IIT Mandi in May-June 2022 on collective excitations and quasiparticles in interacting quantum matter.

Lecture slides

1. Lecture 1 (quasiparticle concept)

2. Lecture 2 (Bohm-Staver phonons in metals)

3. Lecture 3 (longitudinal plasmons in metals)

4. Lecture 4 (transverse plasmons, fermionic quasiparticles)

5. Lecture 5 (quasiparticle stability and decay, interpretation as localization phenomenon in the many-body Hilbert space (i.e. MBL))

6. Lecture 6 (MBL based strategy for assessing quasiparticle stability using FEAST eigensolvers)

7. Lecture 7 (Holstein-Primakoff transformation, spin-waves, magnons in Heisenberg magnets)

8. Lecture 8 (spin flip (magnon) and domain wall excitations in the transverse-field Ising chain; spinons and Majorana fermions)

9. Lecture 9 (Majorana fermions and visons in the honeycomb Kitaev model)

These lecture notes constitute the first part of a ten lecture course on Kondo Physics at the ICTS Condensed Matter Programme in Bangalore in December 2011. The first six lectures, whose notes at provided here, were meant to acquaint the audience (mostly graduate students) with key concepts in Kondo physics. The last four lectures, presented by Prof. Logan, University of Oxford, were devoted to Kondo physics in the context of mesoscopic systems. They are not available here.

Recommended book

A C Hewson, The Kondo problem to Heavy Fermions

Lecture slides (first six)

1. Lecture 1 Introduction to Kondo effect

2. Lecture 2 Perturbation theory

3. Lecture 3 Poor man's scaling

4. Lecture 4 Nozieres Fermi liquid theory, multichannel Kondo effect

5. Lecture 5 Wilson's numerical renormalization group approach - I

6. Lecture 6 Wilson's numerical renormalization group approach - II

1. Lecture 1