Quantum Physics for Scientists and Technologists

PAUL SANGHERA, PHD, is??an educator, scientist, technologist, and entrepreneur. He has worked at world-class laboratories such as CERN in Europe and Nuclear Lab at Cornell, where he participated in designing and conducting experiments to test the quantum theories and models of subatomic particles. Dr. Sanghera is the author of several bestselling books in the fields of science, technology, and project management as well as the author/coauthor of more than 100 research papers on the subatomic particles of matter published in reputed European and American research journals.

• Acknowledgments xvAbout the Author xviiAbout the Tech Editor xixPeriodic Table of the Elements xxiFundamental Physical Constants xxiiiImportant Combinations of Physical Constants xxvPreface: Science, Technology, and Quantum Physics: Mind the Gap xxvii1 First, There was Classical Physics 11.1 Introduction 21.2 Physics and Classical Physics 31.3 The Classical World of Particles 101.4 Physical Quantities 121.5 Newton’s Laws of Motion 151.6 Rotational Motion 181.7 Superposition and Collision of Particles 221.7.1 Superposition 221.7.2 Collision and Scattering 251.8 Classical World of Waves 261.8.1 Periodic Waves 271.8.2 Defining Wave Characteristics 271.9 Reflection, Refraction, and Scattering 301.10 Diffraction and Interference 321.10.1 Diffraction 321.10.2 Interference 341.11 Equation of Wave Motion 351.12 Light: Particle or Wave? 381.13 Understanding Electricity 391.14 Understanding Magnetism 451.14.1 Magnetic Field 451.14.2 Magnetic Flux 471.15 Understanding Electromagnetism 491.15.1 Types of Electromagnetic and Other Waves 491.15.2 Electromagnetic Spectrum 501.16 Maxwell’s Equations 521.17 Confinement, Standing Waves, and Wavegroups 551.17.1 Confinement 551.17.2 Standing Waves 551.17.3 Wavegroups 591.18 Particles and Waves: The Big Picture 621.19 The Four Fundamental Forces of Nature 631.19.1 Gravitational Force 651.19.2 Electromagnetic Force 661.19.3 Weak and Strong Nuclear Forces 671.19.4 Four Fundamental Forces: The Big Picture 681.20 Unification: A Secret to Scientific and Technological Revolutions 691.21 Special Theory of Relativity 721.22 Classical Approach 751.22.1 Separation of Particles and Waves: Either It is a Particle or a Wave 751.22.2 Either It is Here or There: The Certainty 751.22.3 The World is Continuous: Any Value Within a Range is Possible 761.22.4 Common Grounds Among Particles and Waves: A Red Flag 761.23 Summary 771.24 Additional Problems 782 Particle Behavior of Waves 802.1 Introduction 822.2 The Nature of Light: The Big Picture 822.3 Black-Body Radiation 842.3.1 The Classical Collapse 852.3.2 The Quantum Rescue 892.4 The Photoelectric Effect 932.4.1 The Photoelectric Effect: The Experiment 932.4.2 The Classical Collapse 952.4.3 The Quantum Rescue 982.5 X-Ray Diffraction 1032.6 The Compton Effect 1062.7 Living in the Quantum World 1102.7.1 Using Black-Body Radiation 1102.7.2 Using the Photoelectric Effect 1112.7.3 Using Compton Scattering 1132.8 Summary 1142.9 Additional Problems 1153 Wave Behavior of Particles 1173.1 Introduction 1183.2 Particles and Waves: The Big Picture 1183.3 The de Broglie Hypothesis 1203.4 Measuring the Wavelength of Electrons 1253.5 Quantum Confinement 1293.6 The Uncertainty Principle 1333.6.1 Understanding Particle Waves 1333.6.2 Understanding the Uncertainty Principle 1363.6.3 Another Form of the Uncertainty Principle 1403.7 Wave-Particle Duality of Nature 1413.8 Living in the Quantum World 1433.8.1 Seeing the Nanoworld with Electron Waves 1433.8.2 Seeing Nanostructures with the Diffraction of Particle Waves 1453.8.3 Using Atomic Waves to Navigate Your Way 1473.9 Summary 1473.10 Additional Problems 1484 Anatomy of an Atom 1504.1 Introduction 1514.2 Quantum Mechanics of an Atom: The Big Picture 1524.3 Dalton’s Atomic Theory 1534.4 The Structure of an Atom 1544.5 The Classical Collapse of an Atom 1574.6 The Quantum Rescue 1614.6.1 Bohr’s Model 1614.6.2 The Bohr Model Meets the Spectral Series 1654.6.3 Limitations of the Bohr Model 1714.7 Quantum Mechanics of an Atomic Structure 1714.7.1 Principle Energy Levels 1724.7.2 Sublevels 1734.7.3 Electron Orbitals 1734.8 Classical Physics or Quantum Physics: Which One is the True Physics? 1754.9 Living in the Quantum World 1784.9.1 Free Electron Model for Pi Bonding 1784.10 Summary 1804.11 Additional Problems 1805 Principles and Formalism of Quantum Mechanics 1825.1 Introduction 1835.2 Here Comes Quantum Mechanics 1845.3 Wave Function: The Basic Building Block of Quantum Mechanics 1855.3.1 It is All about Information 1865.3.2 Introducing Probability in Science 1865.4 Operators: The Information Extractors 1895.5 Predicting the Measurements 1895.5.1 Expectation Values 1915.5.2 Operators 1935.6 Put It All into an Equation 1965.7 Eigenfunctions and Eigenvalues 1985.8 Double Slit Experiment Revisited 2005.8.1 Double Slit Experiment for Particles 2015.8.2 Chasing the Electron 2025.9 The Quantum Reality 2045.10 Living in the Quantum World 2065.11 Summary 2085.12 Additional Problems 2096 The Anatomy and Physiology of an Equation 2106.1 Introduction 2116.2 The Schrödinger Wave Equation 2116.3 The Schrödinger Equation for a Free Particle 2176.4 Schrödinger Equation for a Particle in a Box 2196.4.1 Setting Up and Solving the Schrödinger Equation 2206.4.2 Here Comes the Energy Quantization 2216.4.3 Exploring the Solutions of the Schrödinger Equation 2246.4.4 The Uncertainty and Correspondence Principles: Revisited 2266.4.5 Quantum Mechanical Tunneling 2286.5 A Particle in a Three-Dimensional Box 2326.6 Harmonic Oscillator 2346.6.1 Understanding Harmonic Motion 2346.6.2 Harmonic Motion in Quantum Mechanics 2386.7 Understanding the Wave Functions of a Harmonic Oscillator 2436.8 Comparing Quantum Mechanical Oscillator with Classical Oscillator 2476.9 Living in the Quantum World 2506.10 Summary 2526.11 Additional Problems 2527 Quantum Mechanics of an Atom 2547.1 Introduction 2557.2 Applying the Schrödinger Equation to the Hydrogen Atom 2577.3 Solving the Schrödinger Equation for the Hydrogen Atom 2607.3.1 Separating the Variables in the Schrödinger Equation 2607.3.2 Solution of the Azimuthal Equation 2627.3.3 Solutions of the Angular Equation 2647.3.4 Solutions of the Radial Equation 2647.3.5 Solutions of the Schrödinger Equation for the Hydrogen Atom: Putting It All Together 2677.4 Finding the Electron 2707.5 Understanding the Quantum Numbers 2737.5.1 The Principal Quantum Number and Energy Radiations 2737.5.2 The Orbital Quantum Number 2767.5.3 Magnetic Quantum Number 2807.6 The Significance of Hydrogen 2827.7 Living in the Quantum World 2827.8 Summary 2847.9 Additional Problems 2868 Quantum Mechanics of Many-Electron Atoms 2878.1 Introduction 2888.2 Two Challenges to Quantum Mechanics: The Periodic Table and the Zeeman Effect 2898.2.1 The Periodic Table of Elements 2908.2.2 The Split Spectral Lines and the Zeeman Effect 2918.3 Introducing the Electron Spin 2928.4 Exclusion Principle 2958.5 Understanding the Atomic Structure 2988.5.1 Understanding Shells, Subshells, and Orbitals 2988.5.2 Understanding the Electron Configuration of Atoms 3018.6 Understanding the Physical Basis of the Periodic Table 3078.6.1 General Trends Across Groups and Periods 3108.6.2 Alkalis and Alkaline Earths 3128.6.3 Transition Metals 3128.6.4 Inert Gases 3138.6.5 Halogens 3138.6.6 Lanthanides and Actinides 3148.7 Completing the Story of Angular Momentum 3148.8 Understanding the Zeeman Effect 3178.9 Living in the Quantum World 3198.10 Summary 3218.11 Additional Problems 3229 Quantum Mechanics of Molecules 3249.1 Introduction 3259.2 A System of Molecules in Motion 3279.3 Bond: The Atomic Bond 3299.4 Diatomic Molecules 3349.5 Rotational States of Molecules 3369.6 Vibrational States of Molecules 3409.7 Combination of Rotations and Vibrations 3449.8 Electronic States of Molecules 3509.9 Living in the Quantum World 3519.10 Summary 3539.11 Additional Problems 35410 Statistical Quantum Mechanics 35610.1 Introduction 35710.2 Statistical Distributions 35810.3 Maxwell–Boltzmann Distribution 36010.4 Molecular Systems with Quantum States 36910.5 Distribution of Vibrational Energies 37110.5.1 Vibrational Energy 37210.5.2 Population Probability of Vibrational States 37310.5.3 Correspondence with Classical Mechanics 37610.6 Distribution of Rotational Energies 37810.6.1 Rotational Energy 37810.6.2 Population Probability of Rotational States 37810.6.3 Correspondence with Classical Mechanics 38010.7 Distribution of Translational Energies 38110.8 Quantum Statistics of Distinguishable Particles: Putting It All Together 38410.9 Quantum Statistics of Indistinguishable Particles 38610.10 Planck’s Radiation Formula 39110.11 Absorption, Emission, and Lasers 39410.12 Bose–Einstein Condensation 39610.13 Living in the Quantum World 39910.14 Summary 40010.15 Additional Problems 40211 Quantum Mechanics: A Thread Runs through It all 40511.1 Introduction 40611.2 Nanoscience and Nanotechnology 40711.2.1 Sciences behind Nanoscience 40711.2.2 You Need to See Them before You Could Control Them 41011.3 Nanoscale Quantum Confinement of Matter 41511.3.1 Buckyballs 41511.3.2 Carbon Nanotubes 41911.3.3 Nanocrystals 42011.3.4 Quantum Dots 42111.3.5 Quantum Mechanics for Nanostructures 42311.3.6 Favoring Balls and Tubes 42511.3.7 Fruits of Quantum Confinement 42511.4 Quick Overview of Microelectronics 42611.4.1 Microelectronics: A Hindsight 42611.4.2 Basics of Microchips 42811.5 Quantum Computing 43211.6 Quantum Biology 43411.6.1 Four Fundamental Nanostructures of Life 43511.6.2 Central Dogma of Molecular Biology 44111.6.3 Sizes of Biological Particles 44211.6.4 Diving Deeper into the Cell with Quantum Mechanics 44411.7 Exploring the Interface of Classical Mechanics and Quantum Mechanics 44911.8 Living in the Quantum World 44911.9 Summary 45111.10 Additional Problems 451Bibliography 453Index 455

"The book presents a rich, self-contained, cohesive, concise, yet comprehensive picture of quantummechanics for senior undergraduate and first-year graduate students, nonphysicists majors,and for those professionals at the forefront of biology, chemistry, engineering, computer science, materials science, nanotechnology, or related fields." (Zentralblatt MATH, 2011)