Synopses & Reviews
KEY BENEFIT: Robert Scherrer's text provides a uniquely accessible and thorough introduction to quantum mechanics for readers. Scherrer carefully develops a solid foundation by recapping on the required math and other basic concepts before developing all the major more advanced topics.
The Origins of Quantum Mechanics, The Problem with Blackbody Radiation, Math Interlude A: Complex Numbers and Linear Operators, The Schrödinger Equation, One-Dimensional Time-Independent, Math Interlude B: Linear Algebra, The Three-Dimensional Time-Independent, Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function, Spin Angular Momentum, Time-Independent Perturbation Theory, The Variational Principle, Time-Dependent Perturbation Theory, Scattering Theory, The Multiparticle Schrödinger Equation, Some Modern Applications of Quantum Mechanics, What Comes Next? Relativistic Quantum Mechanics
KEY MARKET: For all readers interested in quantum mechanics.
About the Author
Robert Scherrer is Chair of the Department of Physics and Astronomy at Vanderbilt University, where he arrived in 2003 following 15 years as a professor of physics at Ohio State University. He received is A.B. in physics from Princeton University, spent two years at Cambridge University on a Marshall Scholarship, and then received his Ph.D. in physics at the University of Chicago. While a professor at Ohio State, Scherrer received the Alumni Award for Distinguished Teaching. His teaching philosophy follows the advice of Hippocrates: “First, do no harm.” He believes that most physics students come to study physics because they find it interesting, and it is the teacher’s job to maintain that interest while navigating the sometimes-difficult subject matter.
Scherrer’s own research is in the area of theoretical cosmology, including the physics of the early universe, dark matter and dark energy, and the large-scale structure of the universe. He lives in Nashville, Tennessee with his wife and five children.
Table of Contents
Table of Contents
1. The Origins of Quantum Mechanics
1.1 Introduction
1.2 Blackbody Radiation
The Problem with Blackbody Radiation
1.3 The Nature of Light
The Photoelectric Effect
The Compton Effect
Is it a Particle or a Wave?
1.4 TheWave Nature of Matter
1.5 The Bohr Atom
1.6 Where do we Stand?
2. Math Interlude A: Complex Numbers and Linear Operators
2.1 Complex Numbers
2.2 Operators
Definition of an Operator
Eigenfunctions and Eigenvalues
3. The Schrödinger Equation
3.1 Derivation of the Schrödinger Equation
3.2 The Meaning of theWave Function
3.3 The Time-Independent Schrödinger Equation
Derivation of the Time-Independent Schrödinger Equation
Qualitative Solutions and the Origin of Quantization
4. One-Dimensional Time-Independent
Schrödinger Equation
4.1 Unbound States: Scattering and Tunneling
Scattering From Step-Function Potentials
4.2 Bound Systems
The Infinite SquareWell
The Harmonic Oscillator Potential
5. Math Interlude B: Linear Algebra
5.1 Properties of Linear Operators
5.2 Vector Spaces
Inner Products
Adjoint and Hermitian Operators
Basis Sets
6. The Three-Dimensional Time-Independent
Schrödinger Equation
6.1 Solution in Rectangular Coordinates
6.2 Angular Momentum
6.3 The Schrödinger Equation in Spherical Coordinates
6.4 The Hydrogen Atom
7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function
7.1 The Matrix Formulation of Linear Operators
7.2 Dirac Notation
7.3 The Dirac Delta Function
8. Spin Angular Momentum
8.1 Spin Operators
8.2 Evidence for Spin
8.3 Adding Angular Momentum
8.4 The Matrix Representation of Spin
8.5 The Stern–Gerlach Experiment
8.6 Spin Precession
8.7 Spin Systems with Two Particles
Noninteracting Spins
Interacting Spins
8.8 Measurement Theory
Hidden Variables
The ManyWorlds Interpretation of Quantum Mechanics
9. Time-Independent Perturbation Theory
9.1 Derivation of Time-Independent Perturbation Theory
9.2 Perturbations to the Atomic Energy Levels
Fine Structure
The Lamb Shift
9.3 The Atom in External Electric or Magnetic Fields
The Atom in an Electric Field: The Stark Effect
The Atom in a Magnetic Field: The Zeeman Effect
10. The Variational Principle
10.1 Variational Principle: Theory
10.2 Variational Principle: Application to the Helium Atom
11. Time-Dependent Perturbation Theory
11.1 Derivation of Time-Dependent Perturbation Theory
11.2 Application: Selection Rules for Electromagnetic Radiation
12. Scattering Theory
12.1 Definition of the Cross Section
12.2 The Born Approximation
12.3 PartialWaves
13. The Multiparticle Schrödinger Equation
13.1 Wave Function for Identical Particles
13.2 Multielectron Atoms
14. Some Modern Applications of Quantum Mechanics
14.1 Magnetic Resonance Imaging
14.2 Quantum Computing
15. What Comes Next? Relativistic Quantum Mechanics
15.1 The Klein–Gordon Equation
Derivation of the Klein–Gordon Equation
Probability Densities and Currents
15.2 The Dirac Equation
Answers and Hints for Selected End-of-Chapter Exercises
Index