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基本説明
Features - Emphasizes basic quantum principles deduced from fundamental experiments; Presents quantum theory in a novel way by using process diagrams as a visual tool; Guides readers from elementary quantum mechanics to aspects of particle physics. Inspired by the work of Nobel Prize laureate Julian Schwinger, this book provides a clear, extensively illustrated introduction to quantum mechanics.
Full Description
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. FeynmanThe 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 MechanicsThis 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 PhysicsThe 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.
Contents
QUANTUM PRINCIPLESPerspective 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 ProblemsFree Particles in One DimensionPhotoelectric EffectCompton EffectUncertainty Relation for PhotonsStability of Ground StatesBohr ModelFourier Transform and Uncertainty RelationsSchroedinger EquationSchroedinger Equation ExampleDirac Delta FunctionsWave Functions and ProbabilityProbability CurrentTime Separable SolutionsCompleteness for Particle StatesParticle Operator PropertiesOperator RulesTime Evolution and Expectation ValuesWrap-UpProblemsSome One-Dimensional Solutions to the Schroedinger 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 SolutionsProblemsHilbert 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 TransformationsSchroedinger and Heisenburg Pictures of Time EvolutionFree Gaussian Wave Packet in the Heisenberg PicturePotentials and the Ehrenfest Theorem ProblemsThree 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 ProblemsGeneralization 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 Schroedinger EquationSpecification of Angular Momentum EigenstatesAngular Momentum Eigenvectors and Spherical HarmonicsCompleteness and Other Properties of Spherical HarmonicsRadial Eigenfunctions ProblemsQUANTUM 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 ProblemsAddition 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 ProblemsSpin 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 Schroedinger EquationReflection and Transmission AmplitudesOne-Dimensional Delta-Function ScatteringStep-Function Potential ScatteringThe Born SeriesThe Three-Dimensional Integral Schroedinger 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 ProblemsConnecting 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 ProblemsAppendix: 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
