Here are my notes and solutions to various problems in R. Shankar’s textbook Principles of Quantum Mechanics, Second Edition. Obviously I can’t offer any guarantee that all the solutions are actually correct, but I’ve given them my best shot.
Shankar’s book covers quantum mechanics at a level somewhat higher than that of Griffiths’s Introduction to Quantum Mechanics, and it’s my hope that it will provide the necessary background for tackling quantum field theory.
Although I’ve found the book very well written and for the most part easy to follow (Shankar’s style is similar to that of Griffiths, so is quite informal), some of the older printings of the book have a large number of typos in them, so do beware. Some of the typos are just misspelled or omitted words in the text, but some are also in the equations.
These solutions are the only ones that I’ve worked out so far, so please don’t ask me to post “the rest of the chapters” as I haven’t worked on those yet. I will get to them eventually.
An errata list is available here, but this seems to apply only to later, corrected printings, so if you have an older printing, you may have to fend for yourself in detecting typos.
Chapter 1 – Mathematical Introduction
1.1.1, 1.1.2, 1.1.3, 1.1.4, 1.1.5, 1.3.1, 1.3.2, 1.3.3, 1.3.4, 1.4.1, 1.4.2, 1.6.1, 1.6.2, 1.6.3, 1.6.4, 1.6.5, 1.6.6, 1.7.1, 1.7.2, 1.8.1, 1.8.2, 1.8.3, 1.8.4, 1.8.5, 1.8.6, 1.8.7, 1.8.8, 1.8.9, 1.8.10, 1.8.11, 1.8.12, 1.9.1, 1.9.2, 1.9.3, 1.10.1, 1.10.2, 1.10.3, 1.10.4
Hadamard’s lemma, Baker-Campbell-Hausdorff formula, Differential operators – matrix elements and hermiticity, Differential operator – eigenvalues and eigenstates, Dirac delta function as limit of a gaussian integral
Chapter 2 – Review of Classical Mechanics
Chapter 4 – The Postulates – a General Discussion
Chapter 5 – Simple Problems in One Dimension
Chapter 6 – The Classical Limit
Chapter 7 – The Harmonic Oscillator
Chapter 8 – The Path Integral Formulation of Quantum Theory
Chapter 9 – The Heisenberg Uncertainty Relations
Chapter 10 – Systems With N Degrees of Freedom
Chapter 11 – Symmetries and their Consequences
Translation operator from passive transformations, Correspondence between classical and quantum transformations, Translational invariance and conservation of momentum, Time translation and conservation of energy, Time reversal, antiunitary operators and Wigner’s theorem
Chapter 12 – Rotation Invariance and Angular Momentum