Principles of Quantum Mechanics [electronic resource] / by R. Shankar.

1. Mathematical Introduction -- 1.1. Linear Vector Spaces: Basics -- 1.2. Inner Product Spaces -- 1.3. Dual Spaces and the Dirac Notation -- 1.4. Subspaces -- 1.5. Linear Operators -- 1.6. Matrix Elements of Linear Operators -- 1.7. Active and Passive Transformations -- 1.8. The Eigenvalue Problem -- 1.9. Functions of Operators and Related Concepts -- 1.10. Generalization to Infinite Dimensions -- 2. Review of Classical Mechanics -- 2.1. The Principle of Least Action and Lagrangian Mechanics -- 2.2. The Electromagnetic Lagrangian -- 2.3. The Two-Body Problem -- 2.4. How Smart Is a Particle? -- 2.5. The Hamiltonian Formalism -- 2.6. The Electromagnetic Force in the Hamiltonian Scheme -- 2.7. Cyclic Coordinates, Poisson Brackets, and Canonical Transformations -- 2.8. Symmetries and Their Consequences -- 3. All Is Not Well with Classical Mechanics -- 3.1. Particles and Waves in Classical Physics -- 3.2. An Experiment with Waves and Particles (Classical) -- 3.3. The Double-Slit Experiment with Light -- 3.4. Matter Waves (de Broglie Waves) -- 3.5. Conclusions -- 4. The Postulates—a General Discussion -- 4.1. The Postulates -- 4.2. Discussion of Postulates I -III -- 4.3. The Schrödinger Equation (Dotting Your i’s and Crossing your ?’s) -- 5. Simple Problems in One Dimension -- 5.1. The Free Particle -- 5.2. The Particle in a Box -- 5.3. The Continuity Equation for Probability -- 5.4. The Single-Step Potential: a Problem in Scattering -- 5.5. The Double-Slit Experiment -- 5.6. Some Theorems -- 6. The Classical Limit -- 7. The Harmonic Oscillator -- 7.1. Why Study the Harmonic Oscillator? -- 7.2. Review of the Classical Oscillator -- 7.3. Quantization of the Oscillator (Coordinate Basis) -- 7.4. The Oscillator in the Energy Basis -- 7.5. Passage from the Energy Basis to the X Basis -- 8. The Path Integral Formulation of Quantum Theory -- 8.1. The Path Integral Recipe -- 8.2. Analysis of the Recipe -- 8.3. An Approximation to U(t) for the Free Particle -- 8.4. Path Integral Evaluation of the Free-Particle Propagator -- 8.5. Equivalence to the Schrödinger Equation -- 8.6. Potentials of the Form V=a + bx + cx2 + d? + ex? -- 9. The Heisenberg Uncertainty Relations -- 9.1. Introduction -- 9.2. Derivation of the Uncertainty Relations -- 9.3. The Minimum Uncertainty Packet -- 9.4. Applications of the Uncertainty Principle -- 9.5. The Energy-Time Uncertainty Relation -- 10. Systems with N Degrees of Freedom -- 10.1. N Particles in One Dimension -- 10.2. More Particles in More Dimensions -- 10.3. Identical Particles -- 11. Symmetries and Their Consequences -- 11.1. Overview -- 11.2. Translational Invariance in Quantum Theory -- 11.3. Time Translational Invariance -- 11.4. Parity Invariance -- 11.5. Time-Reversal Symmetry -- 12. Rotational Invariance and Angular Momentum -- 12.1. Translations in Two Dimensions -- 12.2. Rotations in Two Dimensions -- 12.3. The Eigenvalue Problem of Lz -- 12.4. Angular Momentum in Three Dimensions -- 12.5. The Eigenvalue Problem of L2 and Lz -- 12.6. Solution of Rotationally Invariant Problems -- 13. The Hydrogen Atom -- 13.1. The Eigenvalue Problem -- 13.2. The Degeneracy of the Hydrogen Spectrum -- 13.3. Numerical Estimates and Comparison with Experiment -- 13.4. Multielectron Atoms and the Periodic Table -- 14. Spin -- 14.1. Introduction -- 14.2. What is the Nature of Spin? -- 14.3. Kinematics of Spin -- 14.4. Spin Dynamics -- 14.5. Return of Orbital Degrees of Freedom -- 15. Addition of Angular Momenta -- 15.1. A Simple Example -- 15.2. The General Problem -- 15.3. Irreducible Tensor Operators -- 15.4. Explanation of Some “Accidental” Degeneracies -- 16. Variational and WKB Methods -- 16.1. The Variational Method -- 16.2. The Wentzel-Kramers-Brillouin Method -- 17. Time-Independent Perturbation Theory -- 17.1. The Formalism -- 17.2. Some Examples -- 17.3. Degenerate Perturbation Theory -- 18. Time-Dependent Perturbation Theory -- 18.1. The Problem -- 18.2. First-Order Perturbation Theory -- 18.3. Higher Orders in Perturbation Theory -- 18.4. A General Discussion of Electromagnetic Interactions -- 18.5. Interaction of Atoms with Electromagnetic Radiation -- 19. Scattering Theory -- 19.1. Introduction -- 19.2. Recapitulation of One-Dimensional Scattering and Overview -- 19.3. The Born Approximation (Time-Dependent Description) -- 19.4. Born Again (The Time-Independent Approximation) -- 19.5. The Partial Wave Expansion -- 19.6. Two-Particle Scattering -- 20. The Dirac Equation -- 20.1. The Free-Particle Dirac Equation -- 20.2. Electromagnetic Interaction of the Dirac Particle -- 20.3. More on Relativistic Quantum Mechanics -- 21. Path Integrals—II -- 21.1. Derivation of the Path Integral -- 21.2. Imaginary Time Formalism -- 21.3. Spin and Fermion Path Integrals -- 21.4. Summary -- A.l. Matrix Inversion -- A.2. Gaussian Integrals -- A.3. Complex Numbers.

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 - 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.