Quirky Quantum Concepts - Eric's Physics Web Page
Quirky QuantumConceptsThe Anti-Textbook*By Eric L. MichelsenManuscript Draft ExcerptI hope this manuscript draft excerpt will encourage you to buy the final book:Locally at the UCSD bookstore: Quirky Quantum ConceptsFrom Springer: Quirky Quantum ConceptsFrom Amazon: Quirky Quantum Concepts z z x- z- z- y imaginary x y- z- real z- imaginary y z- z x- x z- z- 1 z- real0.90.80.70.60.50.50.40.30.20.1 y- 0“Quantum Mechanics is a silly theory, perhaps the silliesttheory to come out of the 20th century. The only reason it has anyfollowing at all is that it is completely supported by experiment.” Unknown physicist“We are all agreed that your theory is crazy. The question thatdivides us is whether it is crazy enough to have a chance of beingcorrect.” Niels Bohr“Now in the further development of science, we want morethan just a formula. First we have an observation, then we havenumbers that we measure, then we have a law which summarizesall the numbers. But the real glory of science is that we can find away of thinking such that the law is evident.” Richard Feynman* Physical, conceptual, geometric, and pictorial physics that didn’t fit in your textbook.
physics.ucsd.edu/ emichelsQuirky Quantum Conceptsemichels at physics.ucsd.eduPhysical constants: 2006 values from NIST. For more, see http://physics.nist.gov/cuu/Constants/ .Speed of light in vacuumc 299 792 458 m s–1 (exact)Gravitational constantRelative standard uncertaintyG 6.674 28(67) x 10–11 m3 kg–1 s–2 1.0 x 10–4Boltzmann constantk 1.380 6504(24) x 10–23 J K–1Stefan-Boltzmann constantRelative standard uncertaintyσ 5.670 400(40) x 10–8 W m–2 K–4 7.0 x 10–6Avogadro constantRelative standard uncertaintyNA, L 6.022 141 79(30) x 1023 mol–1 5.0 x 10–8Molar gas constantR 8.314 472(15) J mol-1 K-1calorie4.184 J (exact)Electron massme 9.109 382 15(45) x 10–31 kgProton massmp 1.672 621 637(83) x 10–27 kgProton/electron mass ratiomp/me 1836.152 672 47(80)Elementary chargee 1.602 176 487(40) x 10–19 CElectron g-factorge –2.002 319 304 3622(15)Proton g-factorgp 5.585 694 713(46)Neutron g-factorgN –3.826 085 45(90)Muon massmμ 1.883 531 30(11) x 10–28 kgInverse fine structure constant –1 137.035 999 679(94)Planck constanth 6.626 068 96(33) x 10–34 J sPlanck constant over 2πħ 1.054 571 628(53) x 10–34 J sBohr radiusa0 0.529 177 208 59(36) x 10–10 mBohr magnetonμB 927.400 915(23) x 10–26 J T–112/30/2016 15:04Copyright 2002 - 2012 Eric L. Michelsen. All rights reserved.2 of 149
physics.ucsd.edu/ emichelsQuirky Quantum Conceptsemichels at physics.ucsd.eduTable of Contents0Front/Back Matter. 60.1 Back Cover . 60.2 Dedication . 60.3 Preface. 60.4 Acknowledgements .101Basic Wave Mechanics Concepts .111.1 The Meaning of Science .111.2 Not Your Grandfather’s Physics: Quantum Weirdness .111.3 The Job of Quantum Mechanics .121.3.1 The Premises of Quantum Mechanics .131.3.2 The Success of Quantum Mechanics .131.3.3 The Failure of Quantum Mechanics .141.4 Axioms to Grind: The Foundation of Quantum Mechanics .141.5 Energy and Momentum Are Special .171.6 Complex Numbers .171.6.1 Fundamental Properties of Complex Numbers .171.6.2 Phasors, Rotation in the Complex Plane, and Negative Frequency .211.7 Probability, Density, and Amplitude .231.7.1 Probability of Discrete Events .231.7.2 Probability Density of Continuous Values .231.7.3 Complex (or “Probability”) Amplitude .251.7.4 Averages vs. Expectations .261.8 The Origin of Schrödinger’s Equation .261.8.1 The Wave Equation .261.8.2 Energy, the Hamiltonian, and the Wave Equation .271.9 The Meaning of the Wave-Function .281.9.1 Where Are We, and Where Do We Go From Here? .281.9.2 Gross Anatomy of a Wave Function .291.10 Operators .321.10.1 Linear Operators .341.10.2 Operator Algebra .341.10.3 Operators: What Is the Meaning of This? .361.10.4 Commutators .431.10.5 External Fields .441.11 From Schrödinger to Newton: Deriving F ma .451.12 Measurement and Decoherence .461.13 Why Do Measurements Produce Eigenvalues? .481.14 The Collapse of Quantum Mechanics .502Riding the Wave: More on Wave Mechanics .522.1 Units of Measure .522.2 The Dirac Delta Function .532.3 Dirac Notation .552.3.1 Kets and Bras .552.3.2 Operators in Dirac Notation .572.3.3 Units Revisited .572.3.4 And Now, the Confusing Part .572.4 Covering Your Bases: Decomposition .592.4.1 Countably Infinite Basis Sets .592.4.2 Example: Finite Basis Sets . Error! Bookmark not defined.2.4.3 Back to Kets and Bras. Error! Bookmark not defined.2.4.4 Continuous (or Uncountable) Basis Sets . Error! Bookmark not defined.2.4.5 Mental Projection: Projection Operators and Decomposition Error! Bookmark not defined.12/30/2016 15:04Copyright 2002 - 2012 Eric L. Michelsen. All rights reserved.1 of 149
physics.ucsd.edu/ emichelsQuirky Quantum Conceptsemichels at physics.ucsd.edu2.4.6 A Funny Operator .592.4.7 Countable or Uncountable Doesn’t Mean Much .602.5 Normalize, Schmormalize .602.5.1 Wave-function normalization .612.5.2 Delta-function normalization .612.5.3 Box normalization .612.5.4 Funny Normalization of Radial Wave Functions (and the Like) .612.6 Adjoints .612.6.1 Continuous Adjoint Operators . Error! Bookmark not defined.2.6.2 Evaluating Adjoints . Error! Bookmark not defined.2.6.3 Adjoint Summary .622.7 The WKB Approximation .622.8 Long-Distance Operators .622.8.1 Introduction to Generators .632.8.2 Parity. Error! Bookmark not defined.2.9 Vector Spaces and Hilbert Spaces .632.9.1 Vector Space Overview .642.9.2 Field of Scalars . Error! Bookmark not defined.2.9.3 Group of Vectors . Error! Bookmark not defined.2.9.4 Scalar Field Vector Group Scalar Multiplication Vector Space . Error! Bookmark notdefined.2.9.5 Observations on Vector Spaces . Error! Bookmark not defined.3Introduction to Scattering.653.1 1D Quantum Scattering .653.1.1 1D Scattering: Finite Width Barrier.653.1.2 1D Scattering: Step Potential . Error! Bookmark not defined.3.2 Introduction to 3D Scattering .673.2.1 3D Hard-Target Classical Scattering .673.2.2 Soft-Target Classical Scattering . Error! Bookmark not defined.3.2.3 Wave Scattering: Electromagnetic and Quantum Waves . Error! Bookmark not defined.3.3 3D Quantum Scattering .693.3.1 3D Quantum Scattering Overview .693.3.2 3D Scattering Off a Target: Schrödinger’s Equation .713.3.3 When Is a Potential “Short Range?” . Error! Bookmark not defined.3.3.4 Differential Cross Section from Scattering Amplitude . Error! Bookmark not defined.3.3.5 The Born Approximation . Error! Bookmark not defined.3.4 Partial Wave Method.713.5 The Optical Theorem .733.6 Identical Particle Scattering .743.7 Scattering Conclusion .754Matrix Mechanics .764.1 Finite Dimensional Kets, Bras, and Inner Products.764.2 Finite Dimensional Linear Operators .774.3 Getting to Second Basis: Change of Bases.784.3.1 Transforming Vector Components to a New Basis . Error! Bookmark not defined.4.3.2 The Transformation Matrix is Unitary . Error! Bookmark not defined.4.3.3 Transforming Operators to a New Basis . Error! Bookmark not defined.4.4 Density Matrices .794.4.1 Development of the Density Matrix .804.4.2 Further Properties of Density Matrices . Error! Bookmark not defined.4.4.3 Density Matrix Examples . Error! Bookmark not defined.4.4.4 Density Matrix Summary . Error! Bookmark not defined.5Angular Momentum .815.1 Rotation Notation .8112/30/2016 15:04Copyright 2002 - 2012 Eric L. Michelsen. All rights reserved.2 of 149
physics.ucsd.edu/ emichelsQuirky Quantum Conceptsemichels at physics.ucsd.edu5.2 Dissection of Orbital Angular Momentum .825.2.1 Orbital Angular Momentum as Fluid .825.2.2 Spherical Harmonics as Motion .825.3 Generating Station: A Different Spin on Angular Momentum .825.4 Spin ½ .845.4.1 Spin Kets, Bras, and Inner Products .845.4.2 Spinors For Spin ½ Particles .855.4.3 Climbing the Ladder: Quantization and the Pauli Matrices . Error! Bookmark not defined.5.4.4 Deriving the Pauli Matrices . Error! Bookmark not defined.5.4.5 Matrices, Matrices, Matrices . Error! Bookmark not defined.5.5 Coupling Spin and Position .885.6 Angular Momentum for Arbitrary j.885.7 Addition of Angular Momentum .895.7.1 Two Indefinites Can Make a Definite .905.7.2 Tensor Products .915.7.3 Operators on Tensor Products .925.7.4 Inner Products of Tensor Products. Error! Bookmark not defined.5.7.5 Clebsch-Gordon Coefficients . Error! Bookmark not defined.5.8 Just a Moment: the Landé g-Factor .926Multi-Particle Quantum Mechanics .946.1.1 Multi-Particle Wave-Functions: Distinct Particles .946.1.2 Multi-Particle Wave-Functions: Identical Particles .946.1.3 Multi-Particle Schrödinger Equation .956.1.4 Multi-Particle States With Spin .966.1.5 Symmetry Of Multi-Particle Wave-Functions: Fermions and Bosons .966.2 Atoms .986.2.1 Forget the Bohr Model.
Quirky Quantum Concepts The Anti-Textbook* By Eric L. Michelsen Manuscript Draft Excerpt I hope this manuscript draft excerpt will encourage you to buy the final book:
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According to the quantum model, an electron can be given a name with the use of quantum numbers. Four types of quantum numbers are used in this; Principle quantum number, n Angular momentum quantum number, I Magnetic quantum number, m l Spin quantum number, m s The principle quantum
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1.3.7 Example: quantum teleportation 26 1.4 Quantum algorithms 28 1.4.1 Classical computations on a quantum computer 29 1.4.2 Quantum parallelism 30 1.4.3 Deutsch's algorithm 32 1.4.4 The Deutsch-Jozsa algorithm 34 1.4.5 Quantum algorithms summarized 36 1.5 Experimental quantum information processing 42 1.5.1 The Stern-Gerlach experiment 43
Academic writing is a formal style of writing and is generally written in a more objective way, focussing on facts and not unduly influenced by personal opinions. It is used to meet the assessment requirements for a qualification; the publ ication requirements for academic literature such as books and journals; and documents prepared for conference presentations. Academic writing is structured .
