PH523 - Quantum Mechanics III, Autumn 2016-17

Instructor Name
Prof. Kumar Rao

Course Type
Elective

Prerequisites

Formally none, but suggested prerequisites would be QM I and Special Relativity, knowing QM II and Electromagnetic Theory also helps in some parts

Topics

1.Review of Special Relativity 2.Relativistic Quantum Mechanics: (i) Preview of why a new approach is needed to replace the Schrodinger equation with a relativistically covariant equation and why probability interpretation fails (ii) Klein-Gordon Equation: Derivation, Interpretation as an equation for spin 0 particles, Charge Conjugation, Time Reversal, Two Component Formalism, Pionic Atom (iii) Dirac Equation: Derivation, Interpretation as an equation for spin 1/2 particles, Dirac, Majorana and Weyl spinors, Helicity and Chirality, Gamma Matrix Manipulations, Charge Conjugation, Time Reversal, Hole Interpretation of Positrons, Covariance of Dirac Equation, Bilinear Covariants 3. Scalar Field Theory: Introduction to Lagrangian Field Density, Noether Current, Coupled Oscillators as a Precursor to Field Quantization, Creation and Annihilation Operators, Normal Ordering, Normalization of One Particle States, Perturbation Theory for Interacting Fields, Dyson Series, Klein Gordon Propagator, Feynman Propagator

Books

Relativistic Quantum Mechanics, Walter Greiner, Gauge Theories in Particle Physics, Vol I, Aitchison and Hey, An Introduction To Quantum Field Theory, Peskin and Schroeder (Classic Text) Quantum Field Theory, Lewis Ryder, Field Quantization, Walter Greiner, Quantum Field Theory In A Nutshell, Anthony Zee A Modern Introduction To Quantum Field Theory, Michele Maggiore Quantum Mechanics, A Second Course In Quantum Theory, Rubin Landau Advanced Quantum Mechanics, Franz Schwabl, The above contain highly overlapping content, each delivering it in its own style, 'color' and 'flavor'. Pick one which resonates with you.

Lectures

There was no mandatory attendance, but it is advisable not to miss any lecture since every lecture builds upon previously covered topics and becomes a prerequisite for next lectures. In our case, blackboard was used for about 2/3 of the semester, and owing to lack of time, slides were used to cover the material quicker in the last few weeks. The instructor motivated each topic and gave a hint of the results before going forward with the mathematics, due to which some concepts were repeated over and over again. This took up time but effectively instilled the concepts in the students. 

Assignments

There were 5 assignments or so, which were graded and were a substitute for quizzes. They were fairly easy if you paid attention in class. The instructor didn’t give us our evaluated assignments back. but the solutions were discussed in class though.

Grading

As mentioned above, there were no quizzes and the graded assignments substituted for the quizzes. However, the mid-semester and end-semester were a bit more difficult than the assignments and required firm understanding of the material, the calculations were lengthy and easy to mess up if you did not have an idea of what you are doing, familiarity with index manipulation (tensor notation) and ability to pursue lengthy equations and simplify them is a must for such calculations .

Online study materials

Notes from David Tong; Lectures by Sidney Coleman (also on Youtube, lecture notes )

Follow-up

Theoretical CMP is a nice follow-up on second quantisation.

Although this course may be useful for the course Elementary Particle Physics, it cannot be thought of as a follow up course(one which would continue with QED,QCD etc). There are none at MSc or undergraduate level that I am aware of with a more in depth coverage of QFT which is essential for anyone pursuing theoretical physics. Perhaps there is a PhD course on these topics, but I am not aware of it.

Pro tips

It is possible to do this along with QM2.

This course is a must for those interested in theoretical physics and mathematical physics, however it requires sincerity and diligence on the part of the student. DO NOT take this course if you just want to have a 'chill' elective or are not genuinely interested or if you are not familiar with quantum mechanics and special relativity. The course contents as mentioned online is a rough guide and it is impossible to take the students from level zero to Higgs field and spontaneous symmetry breaking, that said this course attempts to give only a taste of field theory and nowhere near covers any advanced topics in field theory. The sheer complexity of the calculations can be daunting, but always be sure to remember the guiding principles, physical intuition and basic postulates which serves as a light in the darkness.

Personal comments

Do not expect the course to go deep into QFT. The course is an introduction to relativistic wave equations and not exactly a QFT course.

I was disappointed to not have seen QED, Feynman diagrams or the Standard Model which I believed could be introduced at an elementary level in the course (at least QED is at par with the general difficulty level of the course), do not by any means treat this course as comprehensive, instead view it as a glimpse of field theory. Further topics may be studied under a suitable professor as a reading project/SLP.

Respondents - Sandesh Kalantre, Reebhu Bhattacharya

Note: This is a review to help you make a more informed choice about how to study for this course and/or choosing this course. While we've tried to keep it objective and complete, one must keep in mind that students have varying interests, methods of study, and the course itself changes from year to year.