Principles of Quantum Mechanics

This article is about the book by Ramamurti Shankar. For the book by Paul Dirac, see The Principles of Quantum Mechanics.

Principles of Quantum Mechanics

Author	Ramamurti Shankar
Language	English
Subject	Quantum mechanics
Genre	Non-fiction
Published	March 2011 (2nd edition)
Publisher	Plenum Press
Publication place	United States
ISBN	0306447908

Principles of Quantum Mechanics is a textbook by Ramamurti Shankar. The book has been through two editions. It is used in many college courses around the world.

Contents

1. Mathematical Introduction
   1. Linear Vector Spaces: Basics
   2. Inner Product Spaces
   3. Dual Spaces and the Dirac Notation
   4. Subspaces
   5. Linear Operators
   6. Matrix Elements of Linear Operators
   7. Active and Passive Transformations
   8. The Eigenvalue Problem
   9. Functions of Operators and Related Concepts
   10. Generalization to Infinite Dimensions
2. Review of Classical Mechanics
   1. The Principle of Least Action and Lagrangian Mechanics
   2. The Electromagnetic Lagrangian
   3. The Two-Body Problem
   4. How Smart Is a Particle?
   5. The Hamiltonian Formalism
   6. The Electromagnetic Force in the Hamiltonian Scheme
   7. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations
   8. Symmetries and Their Consequences
3. All Is Not Well with Classical Mechanics
   1. Particles and Waves in Classical Physics
   2. An Experiment with Waves and Particles (Classical)
   3. The Double-Slit Experiment with Light
   4. Matter Waves (de Broglie Waves)
   5. Conclusions
4. The Postulates – a General Discussion
   1. The Postulates
   2. Discussion of Postulates I-III
   3. The Schrödinger Equation (Dotting Your i's and Crossing your $\hbar$'s)
5. Simple Problems in One Dimension
   1. The Free Particle
   2. The Particle in a Box
   3. The Continuity Equation for Probability
   4. The Single-Step Potential: a Problem in Scattering
   5. The Double-Slit Experiment
   6. Some Theorems
6. The Classical Limit
7. The Harmonic Oscillator
   1. Why Study the Harmonic Oscillator?
   2. Review of the Classical Oscillator
   3. Quantization of the Oscillator (Coordinate Basis)
   4. The Oscillator in the Energy Basis
   5. Passage from the Energy Basis to the X Basis
8. The Path Integral Formulation of Quantum Theory
   1. The Path Integral Recipe
   2. Analysis of the Recipe
   3. An Approximation to U(t) for the Free Particle
   4. Path Integral Evaluation of the Free-Particle Propagator
   5. Equivalence to the Schrodinger Equation
   6. Potentials of the Form $V=a+bx+cx^{2}+dx+exx$
9. The Heisenberg Uncertainty Relations
   1. Introduction
   2. Derivation of the Uncertainty Relations
   3. The Minimum Uncertainty Packet
   4. Applications of the Uncertainty Principle
   5. The Energy-Time Uncertainty Relation
10. Systems with $N$ Degrees of Freedom
    1. $N$ Particles in One Dimension
    2. More Particles in More Dimensions
    3. Identical Particles
11. Symmetries and Their Consequences
    1. Overview
    2. Translational Invariance in Quantum Theory
    3. Time Translational In variance
    4. Parity Invariance
    5. Time-Reversal Symmetry
12. Rotational Invariance and Angular Momentum
13. The Hydrogen Atom
14. Spin
15. Addition of Angular Momenta
16. Variational and WKB Methods
17. Time-Independent Perturbation Theory
18. Time-Dependent Perturbation Theory
19. Scattering Theory
20. The Dirac Equation
21. Path Integrals – II
22. Appendix

Reviews

Physics Bulletin said about the book, "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of". American Scientist called it "An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner".

See also

• Modern Quantum Mechanics by J. J. Sakurai
• List of textbooks on classical and quantum mechanics