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.

Table of Contents:
QUANTUM PRINCIPLES 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 Problems 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 Wrap-Up Problems Some One-Dimensional Solutions to the Schrödinger Equation Introduction 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 Problems 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 Problems Three Static Approximation Methods Introduction 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 Problems 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 Problems QUANTUM PARTICLES 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 Problems 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 Problems 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 Problems Quantum Particle Scattering Introduction 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 Problems Connecting to the Standard Model Introduction Discrete Symmetries Parity Time Reversal Charge Conjugation Particle Primer Particle Interactions Quantum Electrodynamics Quantum Chromodynamics Weak Interactions Beyond the Standard Model Supersymmetry Superstrings Postlude Helpful Introductory Books on Particle and String Physics More Advanced Books on Particle and String Physics Problems 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 Index