Quantum Mechanics II ( TIFR, February-May 2011)

This is a graduate course at the Tata Institute of Fundamental Research, Mumbai. The course is now over and this page is being preserved as is.

Several textbooks will be used during the course. The five books pictured above (click to enlarge) are among the recommended ones. A list of other quantum mechanics textbooks can be found on the internet.

My favourite Quantum Mechanics textbooks are the two volumes by Claude Cohen-Tannoudji. However, these do not contain some of the topics to be taught in this course, so for those topics I'll have to use other books. The course contents are as follows:

• Path integral formulation
• Variational methods
• WKB approximation
• Time dependent perturbation theory
• Scattering theory
• Semiclassical treatment of radiation

Additionally the recommended special topics are:

• Relativistic wave equations
• Second quantization

• Assignment 1: Assigned 8 March 2011, due 17 March 2011.
• Assignment 2: Assigned 31 March 2011, due 12 April 2011.
• Assignment 3: Assigned 29 April 2011, due 10 May 2011.
• Assignment 4: Assigned 12 May 2011, due 23 May 2011.

These are handwritten notes that I prepare to help me teach the course. Although I usually use them while teaching, there are occasions when I teach something that was not written in the notes, or do not teach something that I had written in the notes. So they are not an accurate record of the course (nor are they intended to be). Also, though each set of notes is roughly matched to a given lecture, it often happens that part of the material written for a given lecture is taught in the following lecture (if I run out of time).

• Revision Lecture 0.1: Spin, Addition of angular momenta: 8 February 2011
  
• Revision Lecture 0.2: Addition of angular momenta and Clebsch-Gordon coefficients: 10 February 2011
  
• Revision Lecture 0.3: Particles in a magnetic field: 15 February 2011
  References: Cohen-Tannoudji Vol 1, Pages 742-764,
  Landau and Lifshitz QM, Pages 455-473.
• Lectures 1 and 2: Path integrals: 17 and 22 February 2011
  References: Feynman and Hibbs, Chapters 1-3,
  Polchinski "String Theory", pages 329-340 (Appendix I: "A short course on path integrals"),
  Peskin and Schroeder "Quantum Field Theory", Pages 275-281,
  Shankar, Pages 223-235.
• Lecture 3: More on path integrals: 23 February 2011
  References: Same as for Lectures 1 and 2.
• Lecture 4: Perturbation theory using path integrals: 8 March 2011
  References: Feynman and Hibbs, Chapter 6.
• Lecture 5: Variational methods: 10 March 2011
  References: Cohen-Tannoudji Vol 2, Pages 1148-1155.
• Lecture 6: Variational methods: hydrogen molecule: 15 March 2011
  References: Cohen-Tannoudji Vol 2, Pages 1169-1185.
• Lecture 7: Path integral formulation of variational method: 17 March 2011
  References: Feynman and Hibbs, Pages 300-310.
• Lecture 8: WKB approximation: 22 March 2011
  References: Landau and Lifshitz QM, Pages 164-170,
  Merzbacher, Pages 113-124.
• Lecture 9: WKB approximation and semi-classical quantisation: 24 March 2011
  References: Landau and Lifshitz QM, Pages 164-175,
  Merzbacher, Pages 113-124 (includes an excellent treatment of Airy functions),
  Pauli Lectures on Physics, Vol 5 (Wave Mechanics), Pages 126-137.
• Lecture 10: WKB approximation and barrier penetration: 29 March 2011
  References: Landau and Lifshitz QM, Pages 179-185,
  Merzbacher, Pages 125-133.
• Lectures 11 and 12: WKB approximation in path integral formalism -- Instantons: 31 March and 5 April 2011
  This file has been revised again on April 13.
  References: Sidney Coleman, "The Uses of Instantons", reprinted in "Aspects of Symmetry", selected Erice lectures of Sidney Coleman, Pages 265-282, as well as Appendices on Pages 340-345.
  
• Notes on the instanton determinant
  References: Sidney Coleman, "The Uses of Instantons", reprinted in "Aspects of Symmetry", selected Erice lectures of Sidney Coleman, Pages 265-282 and (mainly) Appendices 1 and 2 on Pages 340-345.
  
• Guest lecture "Probing electron interactions using electron tunneling" by Pratap Raychaudhuri: 12 April 2011 (PowerPoint file)
• Lecture 13: Time-dependent perturbation theory: 14 April 2011
  References: Cohen-Tannoudji Vol 2, Pages 1285-1299.
• Lecture 14: Time-dependent perturbation theory: Fermi's Golden Rule, atomic transitions: 19 April 2011
  References: Cohen-Tannoudji Vol 2, Pages 1299-1302, 1305-1315.
• Lecture 15: Time-dependent perturbation theory: Atomic transitions, photoelectric effect: 26 April 2011
  References: Cohen-Tannoudji Vol 2, Pages 1304-1315; Shankar: Pages 499-506.
• Lecture 16: Resonant perturbations: 28 April 2011
  References: Cohen-Tannoudji Vol 1, Pages 443-449, Vol 2, Pages 1340-1343.
• Lecture 17: Scattering theory: basics and partial wave expansion: 3 May 2011
  References: Cohen-Tannoudji Vol 2, Pages 903-915, 921-936.
• Lecture 18: Scattering theory: properties of phase shifts: 5 May 2011
  References: Landau and Lifshitz, Pages 507-511; Shankar, Pages 549-550.
• Lecture 19: Scattering theory: Born approximation: 10 May 2011
  References: Shankar, Pages 529-531, 543-545.
• Lecture 20: Scattering theory for identical particles: 12 May 2011
  References: Landau and Lifshitz, Pages 228-231, 567-569.