Reviews from the First Edition: 'An excellent text? The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner' - ("American Scientist"). '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' - ("Physics Bulletin").Reviews of the Second Edition: 'This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details - all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. It would be particularly useful to beginning students and those in allied areas like quantum chemistry' - ("Mathematical Reviews").R. Shankar has introduced major additions and updated key presentations in this second edition of "Principles of Quantum Mechanics". New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: clear, accessible treatment of underlying mathematics; a review of Newtonian, Lagrangian, and Hamiltonian mechanics; student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates; and, unsurpassed coverage of path integrals and their relevance in contemporary physics.The requisite text for advanced undergraduate- and graduate-level students, "Principles of Quantum Mechanics, Second Edition" is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.
1 Mathematical Introduction 1
1.1 Linear Vector Spaces: Basics 1
1.2 Inner Product Spaces 7
1.3 Dual Spaces and the Dirac Notation 11
1.4 Subspaces 17
1.5 Linear Operators 18
1.6 Matrix Elements of Linear Operators 20
1.7 Active and Passive Transformations 29
1.8 The Eigenvalue Problem 30
1.9 Functions of Operators and Related Concepts 54
1.10 Generalization to Infinite Dimensions 57
2 Review of Classical Mechanics 75
2.1 The Principle of Least Action and Lagrangian Mechanics 78
2.2 The Electromagnetic Lagrangian 83
2.3 The Two-Body Problem 85
2.4 How Smart Is a Particle? 86
2.5 The Hamiltonian Formalism 86
2.6 The Electromagnetic Force in the Hamiltonian Scheme 90
2.7 Cyclic Coordinates, Poisson Brackets, and Canonical Transformations 91
2.8 Symmetries and Their Consequences 98
3 All Is Not Well with Classical Mechanics 107
3.1 Particles and Waves in Classical Physics 107
3.2 An Experiment with Waves and Particles (Classical) 108
3.3 The Double-Slit Experiment with Light 110
3.4 Matter Waves (de Broglie Waves) 112
4 The Postulates - a General Discussion 115
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