## Principles of Quantum Mechanics (2nd Edition)

**Author(s):**

R. Shankar

**Publisher:**

Springer

**Pages:**676

**Further Actions:**

**Categories:**

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Paperback - 9781475705782

08 July 2012

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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,...

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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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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.

`An excellent text....The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succint manner.' - American Scientist, from a review of the First Edition