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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 Schr6dinger 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 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 Schr6dinger Equation

 8.6.Potentials ofthe Form V=a+bx+cx2+dx+exx

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 Invarianee 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 0perators

 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

Appendix

 A.1.Matrix Inversion

 A.2.Gaussian Integrals

 A.3.Complex Numbers

 A.4.The iε Prescription

ANSWERS TO SELECTED EXERCISES

TABLE OF CONSTANTS

INDEX