Quantum Physics For Dummies
QuantumPhysicsFORREVISED EDITIONby StevenHolznerWILEYJohn Wiley& Sons, Inc.
Table of ContentsIntroduction1About This Book1Conventions Used in This Book2Foolish AssumptionsHow This Book IsPart I: Small2Organized2World, Huh? Essential Quantum PhysicsHandling Particles3Part II: Bound and Undetermined:in Bound States3Part III:Turning to Angular Momentum and SpinPart IV: Multiple Dimensions: Going 3D with Quantum PhysicsPart V: Group Dynamics: Introducing Multiple Particles3Part VI: The Part of Tens434Icons Used in This Book4Where to Go from Here5Part 1: SmallChapter 1:World, Huh? Essential Quantum PhysicsDiscoveries and Essential QuantumBeingDiscrete: The Trouble withPhysicsBlack-Body Radiation7910First attempt: Wien's FormulaSecond attempt: Rayleigh-Jeans Law12An intuitive12(quantum) leap:12Max Planck's spectrumThe First Pieces: Seeing Light as ParticlesSolving the photoelectric effectScattering lightProofA Dualoff electrons: The14Compton effectpositron? Dirac and pair productionIdentity: LookingYou Can't KnowThe13at Particles asWavesEverything (But You Can Figure the Odds)Quantum physicsand17182020Heisenberg uncertainty principleRolling the dice:16probabilityChapter 2: Entering the Matrix: Welcome to State VectorsYour Own Vectors in HilbertCreatingSpaceMaking Life Easier with Dirac NotationAbbreviating state vectors as ketsWriting the Hermitian conjugate as a braMultiplying bras and kets: A probability of 121232426272829
QuantumPhysics For Dummies, Revised Editionall your bases: Bras and ketsCoveringasbasis-less30state vectorskets30relationships usingUnderstandingGrooving with Operators.Hello, operator: How operators workI expected that: Finding expectation valuesLooking at linear operatorsGoing Hermitian with Hermitian Operators and AdjointssomeForward and Backward:Finding3131333435the Commutator3637CommutingFinding anti-Hermitian operatorsStarting from Scratch and Ending Up with3738HeisenbergEigenvectors and Eigenvalues: They're Naturally Eigentastic!Understanding how they workFinding eigenvectors and eigenvaluesPreparing for the Inversion: Simplifying with Unitary OperatorsComparing Matrix and Continuous RepresentationsGoingcontinuous with calculusDoing theintoaStuck inHandlingEnergy Welts5759inpotential wellsEscaping from potential wellsTrapping Particles in Infinite Square Potential ing the energy levelsNormalizing the wave functionAdding time dependence to wave functionsShifting to symmetric square well potentialsLimited Potential:5157in Potential WellsBinding particles4955Square WellTrapping Particles4652Particles in Bound StatesLooking4552wavePart 11: Bound and Undetermined:Chapter 3: Getting42Takinga62646567Look at Particles and PotentialAssuming the particlehasplenty of energyAssuming the particle doesn't have enoughSteps6869energyHitting the Wall: Particles and Potential BarriersGetting through potential barriers when E V0Getting through potential barriers, even when EParticles Unbound: Solving the Schrodinger Equation7879 for Free ParticlesGetting a physical particle with a wave packetGoing through a Gaussian example74 V081858788
Table of Contentsand Forth with Harmonic OscillatorsChapter 4: BackGrappling with the Harmonic Oscillator HamiltoniansGoing9192classical with harmonic oscillationUnderstanding total energy in quantum oscillationCreation and Annihilation: Introducing the Harmonic Oscillator9394Operatorsp's and q's: Getting theMind yourenergy state equations97Findingthe harmonic oscillator energyPuttingineigenstatesat Harmonic Oscillator99106numberssome9496Finding the EigenstatesUsing a and aT directlyLooking91OperatorsasMatrices108A Jolt of Java: Using Code to Solve the Schrodinger Equation114NumericallyMaking your approximationsBuilding the actual codeRunning the codePart 111:Turningto114116123Angular Momentum and Spin125Chapter 5: Working with Angular Momentumonthe Quantum Level127Ringing the Operators: Round and Round with Angular MomentumFinding Commutators of Lx, Ly, and Lz128Finding the Angular Momentum EigenvaluesDeriving eigenstate equations with Pmax and133Creating the Angular Momentum EigenstatesPminGetting rotational energy of a diatomic moleculeFinding the Eigenvalues of the Raising and Lowering OperatorsInterpreting AngularRoundingIt Out:Momentum with s ofto theof L in\J inSphericalCoordinate System130131133136138139146coordinates149spherical coordinates150sphericalChapter 6: Getting Dizzy with SpinThe Stern-Gerlach Experiment and the Case of the Missing SpotGetting Down and Dirty with Spin and Eigenstates157157159Hello to Fermions and Bosons160Spin Operators: Running Around with Angular MomentumWorking with Spin 'A and Pauli MatricesSpin '/2 matrices161Halves andIntegers: SayingPauli matrices162163165
QuantumPhysics ForDummies, Revised EditionPart IV: Multiple bimensions:urith Quantum PhysicsGoinq 30Chapter 7: Rectangular Coordinates: Solving167Problems169in Three DimensionsSchrodinger Equation: Now in 3D!ProblemsSolving Three-Dimensional Free ParticleThe x, y, and z equationsFinding the total energy equationsolutionAdding time dependence and getting a physicalPotentials3DwithRectangularGetting Squared AwayTheDetermining the energy levelsNormalizing the wave function172173174175177180181183cubic potentialUsingSpringing intoa1691843D Harmonic OscillatorsChapter 8: Solving Problems in Three Dimensions:189Spherical CoordinatesAngle: Choosing Spherical CoordinatesInstead of RectangularTaking a Good Look at Central Potentials in 3DBreaking down the Schrodinger equationThe angular part of i(/(r, 0, )The radial part of \ /(r, 0, )Handling Free Particles in 3D with Spherical CoordinatesThe spherical Bessel and Neumann functionsThe limits for small and large pHandling the Spherical Square Well PotentialA NewInside the square well: 0 r aOutside the square well: r aGetting the armonic Oscillators205Chapter 9: Understanding Hydrogen AtomsComing190to Terms: TheSchrodinger EquationHydrogen AtomSimplifying and Splitting the Schrodinger Equation for Hydrogen205Solving for \]/(R)210for theSolvingfor211y(r)for smallSolving the radial Schrodinger equationSolving the radial Schrodinger equation for largeYou got the power: Putting together the solutionthe radialFixing208equationkeep it finiteallowed energiesr211r212forf(r) to212215of the hydrogen atomFinding theGetting the form of the radial solution of the Schrodingerequation216Some220hydrogen wave functions218
Table of ContentsCalculating the Energy Degeneracy of the Hydrogen AtomQuantum states: Adding a little spinOn the lines: Getting the orbitalsHunting the Elusive ElectronChapter 10: Handling Many lesFloatingTackling SystemsMany DistinguishableJuggling Many Identical ParticlesLosing identitySymmetry and antisymmetryExchange degeneracy: The steady HamiltonianName that composite: Grooving with the symmetrizationandAntisymmetricWave Functionswith Identical Noninteracting ParticlesWave functions ofPart V:237239242242244244245postulateWorking233Swapping particles withsymmetric and antisymmetricBuilding Symmetric228232atomsexchange operatorClassifying226232Considering wave functions and HamiltoniansA Nobel opportunity: Considering multi-electronA Super-Powerful Tool: Interchange Symmetrythe224231Many-Particle Systems, Generally SpeakingOrder matters:222two-particle systems246247248Wave functions of three-or-more-particle systemsIt's Not Come One, Come All: The Pauli Exclusion Principle249Figuring out the Periodic Table251Group Dynamics: IntroducingMultiple ParticlesChapter 11: Giving SystemsaPush: Perturbation TheoryIntroducing Time-Independent Perturbation TheoryWorking with Perturbations to Nondegenerate HamiltoniansA little expansion: Perturbing the equationsMatching the coefficients of A. and simplifying250253255255256257258Finding the first-order corrections259Finding261the second-order correctionsPerturbation Theory to the Test: Harmonic Oscillatorsin Electric FieldsFindingexact solutionsApplying perturbation theoryWorking with Perturbations to Degenerate HamiltoniansTesting Degenerate Perturbation Theory:Hydrogen in Electric FieldsChapter 12: Wham-Blam! Scattering TheoryIntroducing Particle Scattering and Cross Sections262264264269271275275
QuantumPhysicsFor Dummies, Revised Edition277and Lab FramesTranslating between the Center-of-MassFraming the scattering discussionthe scattering angles between framesRelatingTranslating cross sections between the framesof equalTrying a lab-frame example with Tracking277278281massThe incident wave functionRelating the scattering amplitude285Finding the scattering amplitudeThe Born Approximation: Rescuing the Wave EquationExploring the far limits of the wave functionUsing the first Born approximationPutting the Born approximation to workAn Introduction toQuantumPhysics TutorialsQuantum288289290291Grains of Mystique: Quantum PhysicsQuantum Physics Online Version 2.0295295Mechanics295Mechanics Tutorialfor the Layman.296296296Todd K. Timberlake's TutorialPhysics 24/7's286293of Tens13: Ten Quantum284and differentialcross sectionChapter283285The scattered wave functionPart VI: The Part282296TutorialStan Zochowski's PDF Tutorials297Quantum Atom TutorialCollege of St. Benedict's TutorialA Web-Based Quantum Mechanics Course297Chapter 14: Ten Quantum Physics TriumphsWave-Particle297297299299DualityThe Photoelectric Effect299Postulating Spin300Differences between Newton's Laws andQuantum Physics300Heisenberg Uncertainty PrincipleQuantum TunnelingDiscrete Spectra of Atoms300Harmonic Oscillator301Square Wells302Schrodinger's Cat302301301Glossary303Index309
QuantumPhysics For Dummies,Revised Edition PartIV:Multiple bimensions: Goinq 30 urith Quantum Physic
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About the Author Steven Holzner taught Physics at Cornell University for more than a decade, teaching thousands of students. He’s the award-winning author of many books, including Physics For Dummies, Quantum Physics For Dummies, and Differential Equations For Dummies, plus
About the Author Geraldine Woods teaches English and directs the independent study program at the Horace Mann School in New York City. She is the author of more than 50 books, includ-ing English Grammar For Dummies, SAT For Dummies, Research Papers For Dummies, College Admission Essays For Dummies, AP English Literature For Dummies, and AP English Language and Composition For Dummies, all .
The Quantum Nanoscience Laboratory (QNL) bridges the gap between fundamental quantum physics and the engineering approaches needed to scale quantum devices into quantum machines. The team focuses on the quantum-classical interface and the scale-up of quantum technology. The QNL also applies quantum technology in biomedicine by pioneering new
For example, quantum cryptography is a direct application of quantum uncertainty and both quantum teleportation and quantum computation are direct applications of quantum entanglement, the con-cept underlying quantum nonlocality (Schro dinger, 1935). I will discuss a number of fundamental concepts in quantum physics with direct reference to .
