Quantum Principles and Particles

1. Auflage 2012
ISBN: 978-1-4398-3525-8
Verlag: CRC Press

Buch, Englisch, 546 Seiten, Format (B × H): 177 mm x 254 mm, Gewicht: 956 g

Reihe: Textbook Series in Physical Sciences

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.

Zielgruppe

Undergraduate and graduate students in quantum mechanics; students and professionals in physics, engineering, chemistry, materials science, and related fields.

Autoren/Hrsg.

Wilcox, Walter

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Naturwissenschaften Physik Quantenphysik Teilchenphysik

Inhaltsverzeichnis

QUANTUM PRINCIPLES
Perspective and PrinciplesPrelude to Quantum MechanicsStern–Gerlach Experiment Idealized Stern–Gerlach ResultsClassical Model AttemptsWave Functions for Two Physical-Outcome CaseProcess Diagrams, Operators, and Completeness Further Properties of Operators/ModulationOperator ReformulationOperator RotationBra–Ket Notation/Basis StatesTransition AmplitudesThree-Magnet Setup Example—CoherenceHermitian ConjugationUnitary OperatorsA Very Special OperatorMatrix RepresentationsMatrix Wave Function RecoveryExpectation ValuesWrap Up Problems
Free Particles in One DimensionPhotoelectric EffectCompton EffectUncertainty Relation for PhotonsStability of Ground StatesBohr ModelFourier Transform and Uncertainty RelationsSchrödinger EquationSchrödinger Equation ExampleDirac Delta FunctionsWave Functions and ProbabilityProbability CurrentTime Separable SolutionsCompleteness for Particle StatesParticle Operator PropertiesOperator RulesTime Evolution and Expectation ValuesWrap-UpProblems
Some One-Dimensional Solutions to the Schrödinger EquationIntroductionThe Infinite Square Well: Differential SolutionThe Infinite Square Well: Operator SolutionThe Finite Potential Barrier Step PotentialThe Harmonic OscillatorThe Attractive Kronig–Penny ModelBound State and Scattering SolutionsProblems
Hilbert Space and Unitary TransformationsIntroduction and NotationInner and Outer Operator Products Operator–Matrix RelationshipHermitian Operators and EigenketsGram–Schmidt Orthogonalization ProcessCompatible OperatorsUncertainty Relations and Incompatible Operators Simultaneously Measureable OperatorsUnitary Transformations and Change of BasisCoordinate Displacements and Unitary TransformationsSchrödinger and Heisenburg Pictures of Time EvolutionFree Gaussian Wave Packet in the Heisenberg PicturePotentials and the Ehrenfest Theorem Problems
Three Static Approximation MethodsIntroductionTime-Independent Perturbation TheoryExamples of Time-Independent Perturbation TheoryAspects of Degenerate Perturbation TheoryWKB Semiclassical ApproximationUse of the WKB Approximation in Barrier PenetrationUse of the WKB Approximation in Bound StatesVariational Methods Problems
Generalization to Three DimensionsCartesian Basis States and Wave Functions in Three DimensionsPosition/Momentum Eigenket GeneralizationExample: Three-Dimensional Infinite Square WellSpherical Basis StatesOrbital Angular Momentum OperatorEffect of Angular Momentum on Basis StatesEnergy Eigenvalue Equation and Angular MomentumComplete Set of Observables for the Radial Schrödinger EquationSpecification of Angular Momentum EigenstatesAngular Momentum Eigenvectors and Spherical HarmonicsCompleteness and Other Properties of Spherical HarmonicsRadial Eigenfunctions Problems
QUANTUM PARTICLES
The Three-Dimensional Radial EquationRecap of the Situation The Free ParticleThe Infinite Spherical Well Potential The “Deuteron”The Coulomb Potential: Initial ConsiderationsThe Coulomb Potential: 2-D Harmonic Oscillator ComparisonThe Confined Coulombic Model Problems
Addition of Angular MomentaGeneral Angular-Momentum Eigenstate PropertiesCombining Angular Momenta for Two SystemsExplicit Example of Adding Two Spin 1/2 SystemsExplicit Example of Adding Orbital Angular Momentum and Spin 1/2Hydrogen Atom and the Choice of Basis StatesHydrogen Atom and Perturbative Energy Shifts Problems
Spin and StatisticsThe Connection between Spin and StatisticsBuilding Wave Functions with Identical Particles Particle Occupation BasisMore 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 ScatteringIntroductionThe One-Dimensional Integral Schrödinger EquationReflection and Transmission AmplitudesOne-Dimensional Delta-Function ScatteringStep-Function Potential ScatteringThe Born SeriesThe Three-Dimensional Integral Schrödinger EquationThe Helmholtz Equation and Plane WavesCross Sections and the Scattering AmplitudeScattering Phase ShiftsFinite-Range Potential Scattering The Three-Dimensional Born SeriesIdentical Particle ScatteringProton–Proton Scattering Problems
Connecting to the Standard ModelIntroductionDiscrete SymmetriesParityTime ReversalCharge ConjugationParticle PrimerParticle InteractionsQuantum ElectrodynamicsQuantum ChromodynamicsWeak InteractionsBeyond the Standard ModelSupersymmetrySuperstringsPostludeHelpful Introductory Books on Particle and String PhysicsMore Advanced Books on Particle and String Physics Problems
Appendix: Notation Comments and ComparisonsAppendix: Lattice ModelsAppendix: 2-D Harmonic Oscillator Wave Function NormalizationAppendix: Allowed Standard Model InteractionsAppendix: Weak Flavor MixingAppendix: The Ising Model and MoreIndex

Über Autor(innen)

Wilcox, Walter
Walter Wilcox is a professor of physics and graduate program director for the Department of Physics at Baylor University. He earned his Ph.D. in elementary particle physics from UCLA under the guidance of Dr. Julian Schwinger.

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.