Quantum mechanics: a simplified approach
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
CRC Press, Taylor & Francis Group
[2019]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xix, 239 Seiten Diagramme |
| ISBN: | 9781138197268 |
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Datensatz im Suchindex
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| adam_text | Contents Preface.................................................................................................................................................. xiii Author..................................................................................................................................................... xvii Fundamental Constantsand Important Equations.............................................................................. xix Chapter 1 An Introductory History of Quantum Mechanics֊I..................................................... 1 1.1 Classical View of anElectromagnetic Wave..................................................... 1 1.1.1 What Is an Electromagnetic Wave?.....................................................2 1.1.2 What Are the Properties of an Electromagnetic Wave?..................... 3 1.1.3 How Are the Electromagnetic Waves Generated?.............................. 3 1.2 The Black-Body Radiation Paradox................................................................ 4 1.2.1 The Experimental Observations............................................................ 5 1.2.2 The Mathematical Form of the Radiation Function............................ 7 1.3 The Beginning of Quantum Mechanical View.................................................. 9 Problems......................................................................................................................... 10 1.4 The Photoelectric Effect.................................................................................... 11
Problems......................................................................................................................... 14 1.5 The Compton Effect......................................................................................... 14 Problems......................................................................................................................... 16 1.6 Tutorial.............................................................................................................. 17 1.6.1 Photoelectric Effect..............................................................................17 Chapter 2 An Introductory History of Quantum Mechanics-II....................................................21 2.1 De Broglie Matter Waves.................................................................................. 21 Problems......................................................................................................................... 25 2.2 Electron Diffraction.............................................................................................25 Problems......................................................................................................................... 27 2.3 Double-Slit Experiment.................................................................................... 27 Problems......................................................................................................................... 32 2.4 Uncertainty Principle....................................................................................... 32 2.4.1 The
Uncertainty Principle................................................................... 33 2.4.2 A Simple Proof of the UncertaintyPrinciple...................................... 35 2.5 Measurement..................................................................................................... 36 Chapter 3 Formalism........................................................................................................................39 3.1 3.2 Introduction....................................................................................................... 39 Describing a Quantum Mechanical System: Basic Postulates of the Model........................................................................................................... 39 3.2.1 Postulate 1: Defining an Observable................................................. 39 3.2.2 Indeterminacy Associated with the Measurement of an Observable............................................................................................40 vii
Contents viii 3.2.3 Postulate 2: Defining the States Associated with an Observable....................................................................................... 40 3.2.4 Postulate 3: Measurement of an Observable..................................... 41 3.3 Mathematical Foundation................................................................................ 41 3.3.1 State Vector...........................................................................................41 3.3.2 Ket and Bra Space................................................................................42 3.3.3 Multiplication Rules for Ket and Bra..................................................43 3.3.3.1 Inner Product....................................................................... 43 3.3.3.2 Outer Product..................................................................... 43 3.3.3.3 Orthogonality....................................................................... 43 3.3.3.4 Normalization..................................................................... 43 3.3.4 Operators................................................................................................ 45 3.3.5 Base Kets .............................................................................................. 45 3.3.6 Completeness.........................................................................................45 3.3.6.1 Discrete Spectrum................................................................ 48 3.3.6.2 Continuous Spectrum ....................................................... 50
Problems.......................................................................................................................... 50 3.4 Wave Function................................................................................................... 51 3.4.1 Function Space and Hilbert Space...................................................... 51 3.4.2 Eigenfunctions....................................................................................... 53 3.4.2.1 Orthogonal ......................................................................... 53 3.4.2.2 Normal................................................................................ 54 3.4.2.3 Completeness..................................................................... 54 3.4.3 Probability Density.............................................................................. 54 3.4.4 Expectation Value of an Observable..................................................56 3.4.4.1 Position .............................................................................. 56 3.4.4.2 Momentum........................................................................ 57 3.4.4.3 Kinetic Energy.................................................................... 57 Problems.......................................................................................................................... 58 3.5 Dynamical Properties of the System............................................................... 59 3.5.1 Time-Dependent Schrodinger Equation............................................ 59 3.5.2 Time Evolution
Operator..................................................................... 60 3.5.3 Separation of Variables: Time-Independent Schrodinger Equation...........................................................................61 3.5.4 Stationary States................................................................................... 62 Problems.......................................................................................................................... 63 3.6 Conservation of Probability............................................................................. 64 Problem.......................................................................................................................... 65 3.7 Heisenberg Uncertainty Principle.................................................................... 65 3.7.1 Proof of the Uncertainty Principle..................................................... 67 3.7.1.1 The Schwarz Inequality ..................................................... 67 3.7.2 Applications of the Principle.............................................................. 68 3.7.2.1 Heisenberg’s Microscope.................................................. 68 3.7.2.2 Defining Orbits in Atoms.................................................. 69 Problems......................................................................................................................... 70 3.8 Matrix Mechanics............................................................................................. 71 3.9
Tutorials............................................................................................................. 73 3.9.1 Spin-1/2................................................................................................73 3.9.2 Wave Function..................................................................................... 75
Contents Chapter 4 IX Applications of the Formalism-1....................................................................................81 4.1 Introduction....................................................................................................... 81 4.2 The Free Particle.............................................................................................. 81 Problems......................................................................................................................... 86 4.3 The Infinite Square Well.................................................................................. 86 Problems......................................................................................................................... 92 4.4 Step Potential..................................................................................................... 92 Problems......................................................................................................................... 98 4.5 Potential Barrier Penetration(Tunneling)......................................................... 98 Problems....................................................................................................................... 100 4.6 The Finite Square Well.................................................................................. 100 Problems....................................................................................................................... 104 4.7
Tutorials........................................................................................................... 105 4.7.1 Infinite Square Well......................................................................... 105 4.7.2 Tunneling......................................................................................... 110 4.7.3 Quantum Wave Packet.................................................................... 119 Chapter 5 Applications of the Formalism-II.............................................................................. 127 5.1 The Harmonic Oscillator................................................................................ 127 5.1.1 Analytical Method........................................................................... 127 5.1.1.1 Normalization Constant................................................... 131 Problems....................................................................................................................... 133 5.1.2 Algebraic Method............................................................................ 134 5.1.2.1 Normalization Constant................................................. 137 Problems....................................................................................................................... 138 5.2 The Schrodinger Equation in ThreeDimensions.......................................... 138 5.2.1 The Schrodinger Equation in Cartesian Coordinates.................. 138 5.2.1.1 What Is the New Quantum Property of the З-Dimensional Infinite Square Well?............................. 140
Problems....................................................................................................................... 141 5.2.2 The Schrodinger Equation in Spherical Coordinates.................. 141 5.2.3 The Angular Equation..................................................................... 142 5.2.4 The Radial Equation....................................................................... 145 5.3 The Hydrogen Atom....................................................................................... 146 5.3.1 The Radial Equation for the Hydrogen Atom.............................. 147 5.3.1.1 Asymptotic Behavior...................................................... 147 5.3.1.2 PowerSeries Solution..................................................... 148 5.3.1.3 The Lagueire Polynomials and the Associated Laguerre Polynomials.................................................... 151 5.3.1.4 Degeneracy of Hydrogen Atom.................................... 153 5.3.2 Hydrogen Atom Spectrum.............................................................. 153 Problems....................................................................................................................... 156 5.4 The Angular Momentum................................................................................ 156 5.4.1 What Are the Eigenfunctions and Eigenvalues of These Operators?......................................................................... 159 5.4.2 Is Angular Momentum Conserved in a Quantum Mechanical
System?....................................................................... 159
x Contents Problems........................................................................................................................ 161 5.5 Tutorial.............................................................................................................. 62 5.5.1 Angular Momentum ........................................................................ 162 Chapter 6 Perturbation Theory..................................................................................................... 167 6.1 Time-Independent Perturbation....................................................................... 6.1.1 Non-Degenerate Perturbation.......................................................... 6.1.1.1 First-Order Correction..................................................... 6.1.1.2 Second-Order Correction................................................ 6.1.2 Degenerate Perturbation.................................................................. 6.1.2.1 What Is a Degenerate State?......................................... 6.1.3 Stark Effect........................................................................................ 6.1.3.1 Parity.................................................................................. Problems........................................................................................................................ 6.2 The Variational Principle................................................................................. 6.2.1 The Ground State of a Helium Atom.............................................
Problems........................................................................................................................ 6.3 The WKB Method........................................................................................... 6.3.1 Turning Points of a Bound Slate.................................................... Problems........................................................................................................................ Chapter 7 167 168 168 170 170 170 172 172 173 174 176 180 180 186 188 Time-Dependent Perturbation Theory......................................................................... 189 7.1 Introduction...................................................................................................... 189 7.2 First-Order Perturbation Theory.................................................................... 190 7.3 Periodic Perturbations...................................................................................... 193 Problems........................................................................................................................ 194 7.4 The Sudden Approximation........................................................................... 194 Problems........................................................................................................................ 196 7.5 Adiabatic Approximation ............................................................................... 196 7.5.1 Adiabatic Process............................................................................. 197 7.5.2 Adiabatic
Theorem........................................................................... 197 7.5.3 Proof of the Adiabatic Theorem.................................................... 199 Problems..........................................................................................................................202 7.6 Measurement Problem Revisited...................................................................... 202 7.6.1 EPR Paradox.................................................................................... 204 7.6.2 Bell’s Inequality............................................................................... 206 Chapter 8 Quantum Computer......................................................................................................... 209 8.1 8.2 Classical Computer........................................................................................... 209 Quantum Computer........................................................................................... 211 8.2.1 Qubit.................................................................................................. 212 8.2.2 Multiple Qubits................................................................................ 214 8.2.2.1 Entanglement.................................................................... 215 8.2.3 Qubit Gates........................................................................................ 215 Problems..........................................................................................................................217 8.3 Quantum
Algorithms..........................................................................................218
Contents XI 8.4 8.5 Quantum Measurement....................................................................................220 Density Operator.............................................................................................. 222 8.5.1 Properties of a Density Operator.................................................... 223 8.5.2 Reduced Density Operator.............................................................. 224 Problems......................................................................................................................... 224 8.6 Decoherence......................................................................................................224 8.7 Methods for Overcoming Decoherence......................................................... 226 8.7.1 Quantum Error-Correcting Codes.................................................. 226 Problems......................................................................................................................... 228 8.8 Quantum Teleportation..................................................................................... 228 8.9 Superdense Coding...........................................................................................230 References.............................................................................................................................................231 Index ......................................................................................................................................................233
Physics names Quantum mechanics is one of the most challenging subjects to learn. It is challenging because a quantum phenomenon is counterintuitive and the mathe matics used to explain it is often abstract and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas in a step- by- step structured way along with comparisons between quantum and classical concepts that provide clear distinction between classical and quantum logic. Conceptual questions are given after every important section so that readers can check their understanding at every step. Tutorials are included on special topics to teach problem solving by actively engaging readers in a thinking process about the topic. Simulations are provided to aid in the visualization of the quantum phenomenon and to gain meaningful understanding of the mathematics involved. This approach may lead to the development of quantum mechanical intuition as well as a learning of mathematical techniques for problem solving. Most importantly, the book does not contain an overabundance of topics that can make readers confused and distracted, but rather the most important topics are discussed and at a deep level. The story of the development of quantum theory is one of the most inspiring stories in physics. Readers are introduced to the early ideas and experiments that lead to the theory of quantum mechanics in the first two chapters. The key features of this book are: A simplified, structured, and step- by- step introduction to quantum mechanics A systematic arrangement of
topics and chapters Conceptual questions to test logical understanding Tutorials on special topics to actively engage students in a thinking process concerning the differences between quantum mechanics and classical physics Simulations to aid in the visualization of the physical phenomenon with demonstrations of the application of mathematics CRC Press * f’i 1,1 Հ ® ISBN-13: 47fi-l-13fl-1472b-fl 978113819726890000 Taylor Francis Group an informa business www.crcpress.com CRC Press titles are available as eBook editions in a range of digital formats c 106514800664662
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| spelling | Siddiqui, Shabnam Verfasser (DE-588)1177928795 aut Quantum mechanics a simplified approach Shabnam Siddiqui London CRC Press, Taylor & Francis Group [2019] xix, 239 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Quantum theory Textbooks Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031246182&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031246182&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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