Elements of Quantum Mechanics

Description

Elements of Quantum Mechanics provides a solid grounding in the fundamentals of quantum theory and is designed for a first semester graduate or advanced undergraduate course in quantum mechanics for chemistry, chemical engineering, materials science, and physics students. The text includes full development of quantum theory. It begins with the most basic concepts of quantum theory, assuming only that students have some familiarity with such ideas as the uncertainty principle and quantized energy levels. Fayer's accessible approach presents balanced coverage of various quantum theory formalisms, such as the Schr:odinger representation, raising and lowering operator techniques, the matrix representation, and density matrix methods. He includes a more extensive consideration of time dependent problems than is usually found in an introductory graduate course. Throughout the book, sufficient mathematical detail and classical mechanics background are provided to enable students to follow the quantum mechanical developments and analysis of physical phenomena. Fayer provides many examples and problems with fully detailed analytical solutions. Creating a distinctive flavor throughout, Fayer has produced a challenging text with exercises designed to help students become fluent in the concepts and language of modern quantum theory, facilitating their future understanding of more specialized topics. The book concludes with a section containing problems for each chapter that amplify and expand the topics covered in the book. A complete and detailed solution manual is available.

Table of Contents

Preface
Chapter 1. Absolute Size and the Superposition Principle
Chapter 2. Kets, Bras, Operators, and the Eigenvalue Problem
A. Kets and Bras
B. Linear Operators
C. Eigenvalues and Eigenvectors
Chapter 3. Momentum of a Free Particle and Wave Packets
A. Momentum States of a Free Particle
B. Normalization of the Momentum Eigenfunctions
C. Wave Packets
D. Wave Packet Motion and Group Velocities
Chapter 4. Commutators, Dirac's Quantum Condition, and the Uncertainty Principle
A. Dirac's Quantum Condition
B. Commutators and Simultaneous Eigenfunctions
C. Expectation Values and Averages
D. The Uncertainty Principle
Chapter 5. The Schrodinger Equation, Time-Dependent and Time-Independent
A. The Schrodinger Equation
B. The Equation of Motion of the Expectation Value
C. The Free-Particle Energy Eigenvalue Problem
D. The Particle in a Box Energy Eigenvalue Problem
E. Particle in a Finite Box, Tunneling
Chapter 6. The Harmonic Oscillator in the Schrodinger and Dirac Representations
A. The Quantum Harmonic Oscillator in the Schrodinger Representation
B. The Quantum Harmonic Oscillator in the Dirac Represenation
C. Time-Dependent Harmonic Oscillator Wave Packet
Chapter 7. The Hydrogen Atom
A. Separation of the Schrodinger Equation
B. Solutions of the Three One-Dimensional Equations
B. The Hydrogen Atom Wavefunctions
Chapter 8. Time-Dependent Two-State Problem
A. Electronic Excitation Transfer
B. Projection Operators
C. Stationary States
D. The Nondegenerate Case and the Role of Thermal Fluctuations
E. An Infinite System--Excitons
Chapter 9. Perturbation Theory
A. Perturbation Theory for Nondegenerate States
B. Examples--Perturbed Harmonic Oscillator and the Stark Effect for the Rigid Plane Rotor
C. Perturbation Theory for Degenerate States
Chapter 10. The Helium Atom: Perturbation Treatment and the Variation Principle
A. Perturbation Theory Treatment of the Helium Atom Ground State
B. The Variational Theorem
B. Variation Treatment of the Helium Atom Ground State
Chapter 11. Time-Dependent Perturbation Theory
A. Development of Time-Dependent Perturbation
B. Vibrational Excitation by a Grazing Ion-Molecule Collision
Chapter 12. Absorption and Emission of Radiation
A. The Hamiltonian for Charged Particles in Electric and Magnetic Fields
B. Application of Time-Dependent Perturbation Theory
C. Spontaneous Emission
D. Selection Rules
E. Limitations of the Time-Dependent Perturbation Theory Treatment
Chapter 13. The Matrix Representation
A. Matrices and Operators
B. Change of Basis Set
C. Hermitian Operators and Matrices
D. The Harmonic Osciallator in the Matrix Representation
E. Solving the Eigenvalue Problem by Matrix Diagonalization
Chapter 14. The Density Matrix and Coherent Coupling of Molecules to Light
A. The Density Operator and the Density Matrix
B. The Time Dependence of the Density Matrix
C. The Time-Dependent Two-State Problem
D. Expectation Value of an Operator
E. Coherent Coupling of a Two-State System by an Optical Field
F. Free Precession
G. Pure and Mixed Density Matrices
H. The Free Induction Decay
Chapter 15. Angular Momentum
A. Angular Momentum Operators
B. The Eigenvalues of J2 and Jz
C. Angular Momentum Matrices
D. Orbital Angular Momentum and the Zeeman Effect
E. Addition of Angular Momentum
Chapter 16. Electron Spin
A. The Electron Spin Hypothesis
B. Spin-Orbit Coupling
C. Antisymmetrization and the Pauli Principle
D. Singlest and Triplet States
Chapter 17. The Covalent Bond
A. Separation of Electronic and Nuclear Motion: The Born-Oppenheimer Approximation
B. The Hydrogen Molecule Ion
C. The Hydrogen Molecule
Problems
Physical Constants and Conversion Factors for Energy Units
Index