Quantum Principles and Particles: 1st Edition (Paperback) book cover

Quantum Principles and Particles

1st Edition

By Walter Wilcox

CRC Press

546 pages | 142 B/W Illus.

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A Novel Pedagogical Approach to Quantum Mechanics

"A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist."

—R. Feynman

The core of modern physics, quantum theory is counter-intuitive and challenging for those new to the field. Quantum Principles and Particles presents the fundamental quantum principles in a particularly visual manner and applies them to aspects of particle interactions. Inspired by the author’s work with Nobel laureate Julian Schwinger, it introduces the primary principles of the microscopic world through an analysis of the simplest possible quantum mechanical system—spin 1/2.

A Visual Approach to Quantum Mechanics

This two-semester introductory undergraduate textbook balances simplification and rigor to provide an accessible, solid foundation in quantum mechanics. Taking a unique pedagogical approach, the author uses hypothetical quantum devices—process diagrams—to orient and guide the reader. These process diagrams help readers visualize states and operators, and illustrate ways to compute amplitudes for quantum mechanical processes.

From Small Steps in Quantum Mechanics to a Leap into Particle Physics

The first part of the book presents the essential principles in the development of quantum mechanics, starting with spin state analysis and wave mechanics. Delving into quantum particles, the second part develops a consistent picture of particle descriptions and interactions in atomic, nuclear, and particle contexts. The text emphasizes applications and makes the connection to the Standard Model of particle physics. In each chapter, carefully designed problem sets reinforce key principles and stimulate original thought. Extensively illustrated, this classroom-tested text provides a clear and comprehensive introduction to quantum mechanics.


"The fresh student will find a practical guide through quantum mechanics and plenty of problems at the end of each chapter to deepen his or her knowledge with pencil and paper. …For the reader already familiar with quantum mechanics, the textbook offers a fresh collection of model calculations and problems that can be very well used for both personal fun or teaching purposes."

—Adriana Palffy, Contemporary Physics, 2013

"This text contains many innovative features, tricks, and other material not usually found in an undergraduate introduction to quantum mechanics. From beginning the text with simple two state systems to ending it with an introduction to the standard model of particle physics, clearly Wilcox has rethought considerably how an introduction to the field can best be conveyed to undergraduates, and his book is a very welcome addition."

—Professor Donald N. Petcher, Covenant College

Table of Contents


Perspective and Principles

Prelude to Quantum Mechanics

Stern–Gerlach Experiment

Idealized Stern–Gerlach Results

Classical Model Attempts

Wave Functions for Two Physical-Outcome Case

Process Diagrams, Operators, and Completeness

Further Properties of Operators/Modulation

Operator Reformulation

Operator Rotation

Bra–Ket Notation/Basis States

Transition Amplitudes

Three-Magnet Setup Example—Coherence

Hermitian Conjugation

Unitary Operators

A Very Special Operator

Matrix Representations

Matrix Wave Function Recovery

Expectation Values

Wrap Up


Free Particles in One Dimension

Photoelectric Effect

Compton Effect

Uncertainty Relation for Photons

Stability of Ground States

Bohr Model

Fourier Transform and Uncertainty Relations

Schrödinger Equation

Schrödinger Equation Example

Dirac Delta Functions

Wave Functions and Probability

Probability Current

Time Separable Solutions

Completeness for Particle States

Particle Operator Properties

Operator Rules

Time Evolution and Expectation Values



Some One-Dimensional Solutions to the Schrödinger Equation


The Infinite Square Well: Differential Solution

The Infinite Square Well: Operator Solution

The Finite Potential Barrier Step Potential

The Harmonic Oscillator

The Attractive Kronig–Penny Model

Bound State and Scattering Solutions


Hilbert Space and Unitary Transformations

Introduction and Notation

Inner and Outer Operator Products

Operator–Matrix Relationship

Hermitian Operators and Eigenkets

Gram–Schmidt Orthogonalization Process

Compatible Operators

Uncertainty Relations and Incompatible Operators

Simultaneously Measureable Operators

Unitary Transformations and Change of Basis

Coordinate Displacements and Unitary Transformations

Schrödinger and Heisenburg Pictures of Time Evolution

Free Gaussian Wave Packet in the Heisenberg Picture

Potentials and the Ehrenfest Theorem


Three Static Approximation Methods


Time-Independent Perturbation Theory

Examples of Time-Independent Perturbation Theory

Aspects of Degenerate Perturbation Theory

WKB Semiclassical Approximation

Use of the WKB Approximation in Barrier Penetration

Use of the WKB Approximation in Bound States

Variational Methods


Generalization to Three Dimensions

Cartesian Basis States and Wave Functions in Three Dimensions

Position/Momentum Eigenket Generalization

Example: Three-Dimensional Infinite Square Well

Spherical Basis States

Orbital Angular Momentum Operator

Effect of Angular Momentum on Basis States

Energy Eigenvalue Equation and Angular Momentum

Complete Set of Observables for the Radial Schrödinger Equation

Specification of Angular Momentum Eigenstates

Angular Momentum Eigenvectors and Spherical Harmonics

Completeness and Other Properties of Spherical Harmonics

Radial Eigenfunctions



The Three-Dimensional Radial Equation

Recap of the Situation

The Free Particle

The Infinite Spherical Well Potential

The “Deuteron”

The Coulomb Potential: Initial Considerations

The Coulomb Potential: 2-D Harmonic Oscillator Comparison

The Confined Coulombic Model


Addition of Angular Momenta

General Angular-Momentum Eigenstate Properties

Combining Angular Momenta for Two Systems

Explicit Example of Adding Two Spin 1/2 Systems

Explicit Example of Adding Orbital Angular Momentum and Spin 1/2

Hydrogen Atom and the Choice of Basis States

Hydrogen Atom and Perturbative Energy Shifts


Spin and Statistics

The Connection between Spin and Statistics

Building Wave Functions with Identical Particles

Particle Occupation Basis

More on Fermi–Dirac Statistics

Interaction Operator and Feynman Diagrams

Implications of Detailed Balance

Cubical Enclosures and Particle States

Maxwell–Boltzmann Statistics

Bose–Einstein Statistics

Fermi–Dirac Statistics

The Hartree–Fock Equations


Quantum Particle Scattering


The One-Dimensional Integral Schrödinger Equation

Reflection and Transmission Amplitudes

One-Dimensional Delta-Function Scattering

Step-Function Potential Scattering

The Born Series

The Three-Dimensional Integral Schrödinger Equation

The Helmholtz Equation and Plane Waves

Cross Sections and the Scattering Amplitude

Scattering Phase Shifts

Finite-Range Potential Scattering

The Three-Dimensional Born Series

Identical Particle Scattering

Proton–Proton Scattering


Connecting to the Standard Model


Discrete Symmetries


Time Reversal

Charge Conjugation

Particle Primer

Particle Interactions

Quantum Electrodynamics

Quantum Chromodynamics

Weak Interactions

Beyond the Standard Model




Helpful Introductory Books on Particle and String Physics

More Advanced Books on Particle and String Physics


Appendix: Notation Comments and Comparisons

Appendix: Lattice Models

Appendix: 2-D Harmonic Oscillator Wave Function Normalization

Appendix: Allowed Standard Model Interactions

Appendix: Weak Flavor Mixing

Appendix: The Ising Model and More


About the Author

Walter Wilcox is professor of physics and graduate program director for the Baylor University Physics Department. He earned a PhD in elementary particle physics from UCLA in 1981 under the guidance of Dr. Julian Schwinger. He has also taught and done research at Oklahoma State University (1981–1983), TRIUMF Laboratory (1983-1985), and the University of Kentucky (1985–1986). He has been awarded grants from the National Science Foundation (NSF) in theoretical physics and, in collaboration with Ron Morgan, in applied mathematics. His research focuses on the development and use of numerical methods in the field of theoretical physics known as "lattice QCD". He lives in Waco, Texas, and loves to go hiking and camping.

For more information about Dr. Wilcox’s work, see Dr. Wilcox’s web site at Baylor University.

About the Series

Textbook Series in Physical Sciences

This textbook series offers pedagogical resources for the physical sciences. It publishes high-quality, high-impact texts to improve understanding of fundamental and cutting edge topics, as well as to facilitate instruction. The authors are encouraged to incorporate numerous problems and worked examples, as well as making available solutions manuals for undergraduate and graduate level course adoptions. The format makes these texts useful as professional self-study and refresher guides as well. Subject areas covered in this series include condensed matter physics, quantum sciences, atomic, molecular, and plasma physics, energy science, nanoscience, spectroscopy, mathematical physics, geophysics, environmental physics, and so on, in terms of both theory and experiment.

New books in the series are commissioned by invitation. Authors are also welcome to contact the publisher (Lou Chosen, Executive Editor: lou.chosen@taylorandfrancis.com) to discuss new title ideas.

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics
SCIENCE / Quantum Theory