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: Locally at the UCSD bookstore: Quirky Quantum Concepts From Springer: Quirky Quantum Concepts From Amazon: Quirky Quantum Concepts |z-> |z-> imaginary |z+> 1 |y+> imaginary |y+> 0.9 |z-> 0.8 |z+> 0.7 |x+> |z+> |z-> 0.6 |x-> |x-> |x+> 0.5 0.5 |y-> |z-> real 0.4 real 0.3 |y-> |z-> |z-> 0.2 |z-> 0.1 0 “Quantum Mechanics is a silly theory, perhaps the silliest theory to come out of the 20th century. The only reason it has any following at all is that it is completely supported by experiment.” − Unknown physicist “We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.” − Niels Bohr “Now in the further development of science, we want more than just a formula. First we have an observation, then we have numbers that we measure, then we have a law which summarizes all the numbers. But the real glory of science is that we can find a way 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/~emichels Quirky Quantum Concepts emichels at physics.ucsd.edu Physical constants: 2006 values from NIST. For more, see http://physics.nist.gov/cuu/Constants/ . Speed of light in vacuum c = 299 792 458 m s–1 (exact) Gravitational constant G = 6.674 28(67) x 10–11 m3 kg–1 s–2 Relative standard uncertainty ±1.0 x 10–4 Boltzmann constant k = 1.380 6504(24) x 10–23 J K–1 Stefan-Boltzmann constant σ = 5.670 400(40) x 10–8 W m–2 K–4 –6 Relative standard uncertainty ±7.0 x 10 23 –1 Avogadro constant NA, L = 6.022 141 79(30) x 10 mol Relative standard uncertainty ±5.0 x 10–8 Molar gas constant R = 8.314 472(15) J mol-1 K-1 calorie 4.184 J (exact) –31 Electron mass me = 9.109 382 15(45) x 10 kg –27 Proton mass mp = 1.672 621 637(83) x 10 kg Proton/electron mass ratio mp/me = 1836.152 672 47(80) Elementary charge e = 1.602 176 487(40) x 10–19 C Electron g-factor ge = –2.002 319 304 3622(15) Proton g-factor gp = 5.585 694 713(46) Neutron g-factor gN = –3.826 085 45(90) –28 Muon mass mμ = 1.883 531 30(11) x 10 kg Inverse fine structure constant –1 = 137.035 999 679(94) Planck constant h = 6.626 068 96(33) x 10–34 J s Planck constant over 2π ħ = 1.054 571 628(53) x 10–34 J s –10 Bohr radius a0 = 0.529 177 208 59(36) x 10 m –26 –1 Bohr magneton μB = 927.400 915(23) x 10 J T 12/30/2016 15:04 Copyright 2002 - 2012 Eric L. Michelsen. All rights reserved. 2 of 149 physics.ucsd.edu/~emichels Quirky Quantum Concepts emichels at physics.ucsd.edu Table of Contents 0 Front/Back Matter ................................................................................................................................ 6 0.1 Back Cover ....................................................................................................................................... 6 0.2 Dedication ........................................................................................................................................ 6 0.3 Preface .............................................................................................................................................. 6 0.4 Acknowledgements .........................................................................................................................10 1 Basic Wave Mechanics Concepts .......................................................................................................11 1.1 The Meaning of Science ..................................................................................................................11 1.2 Not Your Grandfather’s Physics: Quantum Weirdness ...................................................................11 1.3 The Job of Quantum Mechanics ......................................................................................................12 1.3.1 The Premises of Quantum Mechanics ...................................................................................13 1.3.2 The Success of Quantum Mechanics .....................................................................................13 1.3.3 The Failure of Quantum Mechanics ......................................................................................14 1.4 Axioms to Grind: The Foundation of Quantum Mechanics ............................................................14 1.5 Energy and Momentum Are Special ...............................................................................................17 1.6 Complex Numbers ..........................................................................................................................17 1.6.1 Fundamental Properties of Complex Numbers ......................................................................17 1.6.2 Phasors, Rotation in the Complex Plane, and Negative Frequency .......................................21 1.7 Probability, Density, and Amplitude ...............................................................................................23 1.7.1 Probability of Discrete Events ...............................................................................................23 1.7.2 Probability Density of Continuous Values ............................................................................23 1.7.3 Complex (or “Probability”) Amplitude .................................................................................25 1.7.4 Averages vs. Expectations .....................................................................................................26 1.8 The Origin of Schrödinger’s Equation ............................................................................................26 1.8.1 The Wave Equation ...............................................................................................................26 1.8.2 Energy, the Hamiltonian, and the Wave Equation .................................................................27 1.9 The Meaning of the Wave-Function ...............................................................................................28 1.9.1 Where Are We, and Where Do We Go From Here? .............................................................28 1.9.2 Gross Anatomy of a Wave Function ......................................................................................29 1.10 Operators .........................................................................................................................................32 1.10.1 Linear Operators ....................................................................................................................34 1.10.2 Operator Algebra ...................................................................................................................34 1.10.3 Operators: What Is the Meaning of This? ..............................................................................36 1.10.4 Commutators .........................................................................................................................43 1.10.5 External Fields .......................................................................................................................44 1.11 From Schrödinger to Newton: Deriving F = ma .............................................................................45 1.12 Measurement and Decoherence ......................................................................................................46 1.13 Why Do Measurements Produce Eigenvalues? ...............................................................................48 1.14 The Collapse of Quantum Mechanics .............................................................................................50 2 Riding the Wave: More on Wave Mechanics ....................................................................................52 2.1 Units of Measure .............................................................................................................................52 2.2 The Dirac Delta Function ................................................................................................................53 2.3 Dirac Notation .................................................................................................................................55 2.3.1 Kets and Bras .........................................................................................................................55 2.3.2 Operators in Dirac Notation ...................................................................................................57 2.3.3 Units Revisited ......................................................................................................................57 2.3.4 And Now, the Confusing Part ................................................................................................57 2.4 Covering Your Bases: Decomposition ............................................................................................59 2.4.1 Countably Infinite Basis Sets .................................................................................................59 2.4.2 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