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Elements of Quantum Mechanics

 

Michael D. Fayer
Stanford University

 

New York · Oxford
Oxford University Press
2001

 

Errata and Addenda

TABLE OF CONTENTS:

Preface			ix
Chapter 1 - Absolute Size and the Superposition Principle			1
Chapter 2 - Kets, Bras, Operators, and the Eigenvalue Problem			7
	A. Kets and Bras		7
	B. Linear Operators		11
	C. Eigenvalues and Eigenvectors		13
Chapter 3 - Momentum of a Free Particle and Wave Packets			18
	A. Momentum States of a Free Particle		19
	B. Normalization of the Momentum Eigenfunctions		20
	C. Wave Packets		23
	D. Wave Packet Motion and Group Velocities		29
Chapter 4 - Commutators, Dirac's Quantum Condition, and the Uncertainty Principle			34
	A. Dirac's Quantum Condition		34
	B. Commutators and Simultaneous Eigenfunctions		36
	C. Expectation Values and Averages		39
	D. The Uncertainty Principle		42
Chapter 5 - The Schrödinger Equation, Time Dependent and Time Independent			45
	A. The Schrödinger Equation		45
	B. The Equation of Motion of the Expectation Value		48
	C. The Free Particle Energy Eigenvalue Problem		49
	D. The Particle in a Box Energy Eigenvalue Problem		51
	E. Particle in a Finite Box, Tunneling and Ionization		57
Chapter 6 - The Harmonic Oscillator in the Schrödinger and Dirac Representations			66
	A. The Quantum Harmonic Oscillator in the Schrödinger Representation		67
	B. The Quantum Harmonic Oscillator in the Dirac Representation		79
	C. Time Dependent Harmonic Oscillator Wave Packet		90
Chapter 7 - The Hydrogen Atom			93
	A. Separation of the Schrödinger Equatio		93
	B. Solutions of the Three One Dimensional Equations		97
	C. The Hydrogen Atom Wavefunctions		105
Chapter 8 - Time Dependent Two State Problem			112
	A. Electronic Excitation Transfer		116
	B. Projection Operators		119
	C. Stationary States		120
	D. The Non-degenerate Case and the Role of Thermal Fluctuations		123
	E. An Infinite System – Excitons		125
Chapter 9 - Perturbation Theory			133
	A. Perturbation Theory for Non-degenerate States		133
	B. Examples – Perturbed Harmonic Oscillator and the Stark Effect for the Rigid Plane Rotor		139
	C. Perturbation Theory for Degenerate		145
Chapter 10 - The Helium Atom: Perturbation Treatment and the Variation Principle			152
	A. Perturbation Theory Treatment of the Helium Atom Ground State		152
	B. The Variational Theorem		158
	C. Variation Treatment of the Helium Atom Ground State		160
Chapter 11 - Time Dependent Perturbation Theory			163
	A. Development of Time Dependent Perturbation Theory		163
	B. Vibrational Excitation by a Grazing Ion-Molecule Collision		165
Chapter 12 - Absorption and Emission of Radiation			172
	A. The Hamiltonian for Charged Particles in Electric and Magnetic Fields		173
	B. Application of Time Dependent Perturbation Theory		178
	C. Spontaneous Emission		186
	D. Selection Rules		188
	E. Limitations of the Time Dependent Perturbation Theory Treatment		189
Chapter 13 - The Matrix Representation			193
	A. Matrices and Operators		193
	B. Change of Basis Set		199
	C. Hermitian Operators and Matrices		204
	D. The Harmonic Oscillator in the Matrix Representation		205
	E. Solving the Eigenvalue Problem by Matrix Diagonalization		208
Chapter 14 - The Density Matrix and Coherent Coupling of Molecules to Light			213
	A. The Density Operator and the Density Matrix		213
	B. The Time Dependence of the Density Matrix		214
	C. The Time Dependent Two State Problem		217
	D. Expectation Value of an Operator		219
	E. Coherent Coupling of a Two State System by an Optical Field		221
	F. Free Precession		226
	G. Pure and Mixed Density Matrices		228
	H. The Free Induction Decay		229
Chapter 15 - Angular Momentum			232
	A. Angular Momentum Operators		232
	B. The Eigenvalues of J2 and Jz		236
	C. Angular Momentum Matrices		240
	D. Orbital Angular Momentum and the Zeeman Effect		242
	E. Addition of Angular Momentum		246
Chapter 16 - Electron Spin			255
	A. The Electron Spin Hypothesis		256
	B. Spin-Orbit Coupling		258
	C. Antisymmetrization and the Pauli Principle		268
	D. Singlet and Triplet States		278
Chapter 17 - The Covalent Bond			280
	A. Separation of Electronic and Nuclear Motion: The Born-Oppenheimer Approximation		280
	B. The Hydrogen Molecule Ion		282
	C. The Hydrogen Molecule		288
Problems			295
Physical Constants and Conversion Factors for Energy Units			314
Index			315