Principles Of Quantum Mechanics (Second Edition)

R. Shankar

Verlag: Springer Publisher, 2015
ISBN 10: 8181286863 / ISBN 13: 9788181286864
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Table of Contents 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 Schrodinger Equation (Dotting Your i`s andCrossing your h`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 Harmonic Oscillator 7. The Classical Limit 7.1. Why Study the Harmonic Oscillator9 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 Schrodinger 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 L, 12.4. Angular Momentum in Three Dimensions 12.5. The Eigenvalue Problem of L2 and L. 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 Electro Printed Pages: 675. Buchnummer des Verkäufers

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Inhaltsangabe: Publish and perish-Giordano Bruno Given the number of books that already exist on the subject of quantum mechanics, one would think that the public needs one more as much as it does, say, the latest version of the Table of Integers. But this does not deter me (as it didn't my predecessors) from trying to circulate my own version of how it ought to be taught. The approach to be presented here (to be described in a moment) was first tried on a group of Harvard under­ graduates in the summer of '76, once again in the summer of '77, and more recently at Yale on undergraduates ('77-'78) and graduates ('78-'79) taking a year-long course on the subject. In all cases the results were very satisfactory in the sense that the students seemed to have learned the subject well and to have enjoyed the presentation. It is, in fact, their enthusiastic response and encouragement that convinced me of the soundness of my approach and impelled me to write this book. The basic idea is to develop the subject from its postulates, after ad­ dressing some indispensable preliminaries.

Klappentext:

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.

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Bibliografische Details

Titel: Principles Of Quantum Mechanics (Second ...
Verlag: Springer Publisher
Erscheinungsdatum: 2015
Einband: Softcover
Zustand: New
Auflage: 5th or later edition.

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