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Introductory Quantum Mechanics with MATLAB


Introductory Quantum Mechanics with MATLAB

For Atoms, Molecules, Clusters, and Nanocrystals
1. Aufl.

von: James R. Chelikowsky

74,99 €

Verlag: Wiley-VCH
Format: EPUB
Veröffentl.: 24.08.2018
ISBN/EAN: 9783527655007
Sprache: englisch
Anzahl Seiten: 224

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Beschreibungen

Presents a unique approach to grasping the concepts of quantum theory with a focus on atoms, clusters, and crystals <br> <br> Quantum theory of atoms and molecules is vitally important in molecular physics, materials science, nanoscience, solid state physics and many related fields. Introductory Quantum Mechanics with MATLAB is designed to be an accessible guide to quantum theory and its applications. The textbook uses the popular MATLAB programming language for the analytical and numerical solution of quantum mechanical problems, with a particular focus on clusters and assemblies of atoms. <br> <br> The textbook is written by a noted researcher and expert on the topic who introduces density functional theory, variational calculus and other practice-proven methods for the solution of quantum-mechanical problems. This important guide: <br> <br> -Presents the material in a didactical manner to help students grasp the concepts and applications of quantum theory <br> -Covers a wealth of cutting-edge topics such as clusters, nanocrystals, transitions and organic molecules <br> -Offers MATLAB codes to solve real-life quantum mechanical problems <br> <br> Written for master's and PhD students in physics, chemistry, material science, and engineering sciences, Introductory Quantum Mechanics with MATLAB contains an accessible approach to understanding the concepts of quantum theory applied to atoms, clusters, and crystals. <br>
<p>Preface xi</p> <p><b>1 Introduction 1</b></p> <p>1.1 Different Is Usually Controversial 1</p> <p>1.2 The Plan: Addressing Dirac’s Challenge 2</p> <p>Reference 4</p> <p><b>2 The Hydrogen Atom 5</b></p> <p>2.1 The Bohr Model 5</p> <p>2.2 The Schrödinger Equation 8</p> <p>2.3 The Electronic Structure of Atoms and the Periodic Table 15</p> <p>References 18</p> <p><b>3 Many-electron Atoms 19</b></p> <p>3.1 The Variational Principle 19</p> <p>3.1.1 Estimating the Energy of a Helium Atom 21</p> <p>3.2 The Hartree Approximation 22</p> <p>3.3 The Hartree–Fock Approximation 25</p> <p>References 27</p> <p><b>4 The Free Electron Gas 29</b></p> <p>4.1 Free Electrons 29</p> <p>4.2 Hartree–Fock Exchange in a Free Electron Gas 35</p> <p>References 36</p> <p><b>5 Density Functional Theory 37</b></p> <p>5.1 Thomas–Fermi Theory 37</p> <p>5.2 The Kohn–Sham Equation 40</p> <p>References 43</p> <p><b>6 Pseudopotential Theory 45</b></p> <p>6.1 The Pseudopotential Approximation 45</p> <p>6.1.1 Phillips–Kleinman CancellationTheorem 47</p> <p>6.2 PseudopotentialsWithin Density FunctionalTheory 50</p> <p>References 57</p> <p><b>7 Methods for Atoms 59</b></p> <p>7.1 The Variational Approach 59</p> <p>7.1.1 Estimating the Energy of the Helium Atom. 59</p> <p>7.2 Direct Integration 63</p> <p>7.2.1 Many-electron Atoms Using Density FunctionalTheory 67</p> <p>References 69</p> <p><b>8 Methods for Molecules, Clusters, and Nanocrystals 71</b></p> <p>8.1 The H2 Molecule: Heitler–LondonTheory 71</p> <p>8.2 General Basis 76</p> <p>8.2.1 PlaneWave Basis 79</p> <p>8.2.2 PlaneWaves Applied to Localized Systems 87</p> <p>8.3 Solving the Eigenvalue Problem 89</p> <p>8.3.1 An Example Using the Power Method 92</p> <p>References 95</p> <p><b>9 Engineering Quantum Mechanics 97</b></p> <p>9.1 Computational Considerations 97</p> <p>9.2 Finite Difference Methods 99</p> <p>9.2.1 Special DiagonalizationMethods: Subspace Filtering 101</p> <p>References 104</p> <p><b>10 Atoms 107</b></p> <p>10.1 Energy levels 107</p> <p>10.2 Ionization Energies 108</p> <p>10.3 Hund’s Rules 110</p> <p>10.4 Excited State Energies and Optical Absorption 113</p> <p>10.5 Polarizability 122</p> <p>References 124</p> <p><b>11 Molecules 125</b></p> <p>11.1 Interacting Atoms 125</p> <p>11.2 Molecular Orbitals: Simplified 125</p> <p>11.3 Molecular Orbitals: Not Simplified 130</p> <p>11.4 Total Energy of a Molecule from the Kohn–Sham Equations 132</p> <p>11.5 Optical Excitations 137</p> <p>11.5.1 Time-dependent Density FunctionalTheory 138</p> <p>11.6 Polarizability 140</p> <p>11.7 The Vibrational Stark Effect in Molecules 140</p> <p>References 150</p> <p><b>12 Atomic Clusters 153</b></p> <p>12.1 Defining a Cluster 153</p> <p>12.2 The Structure of a Cluster 154</p> <p>12.2.1 Using Simulated Annealing for Structural Properties 155</p> <p>12.2.2 Genetic Algorithms 159</p> <p>12.2.3 Other Methods for Determining Structural Properties 162</p> <p>12.3 Electronic Properties of a Cluster 164</p> <p>12.3.1 The Electronic Polarizability of Clusters 164</p> <p>12.3.2 The Optical Properties of Clusters 166</p> <p>12.4 The Role of Temperature on Excited-state Properties 167</p> <p>12.4.1 Magnetic Clusters of Iron 169</p> <p>References 174</p> <p><b>13 Nanocrystals 177</b></p> <p>13.1 Semiconductor Nanocrystals: Silicon 179</p> <p>13.1.1 Intrinsic Properties 179</p> <p>13.1.1.1 Electronic Properties 179</p> <p>13.1.1.2 Effective MassTheory 184</p> <p>13.1.1.3 Vibrational Properties 187</p> <p>13.1.1.4 Example of VibrationalModes for Si Nanocrystals 188</p> <p>13.1.2 Extrinsic Properties of Silicon Nanocrystals 190</p> <p>13.1.2.1 Example of Phosphorus-Doped Silicon Nanocrystals 191</p> <p>References 197</p> <p>A Units 199</p> <p>B A Working Electronic Structure Code 203</p> <p>References 206</p> <p>Index 207</p>
<p><b><i>James Chelikowsky, PhD,</i></b> <i>holds the W.A. "Tex" Moncrief Chair at the University of Texas at Austin. He is a professor in the departments of physics, chemistry and chemical engineering. He also serves as the Director for the Center of Computational Materials in the Institute for Computational Engineering and Sciences.</i>
<p><b>Presents a unique approach to grasping the concepts of quantum theory with a focus on atoms, clusters, and crystals</b> <p>Quantum theory of atoms and molecules plays a vitally important role in molecular physics, materials science, nanoscience, solid state physics and many related fields. <i>Introductory Quantum Mechanics with MATLAB<sup>®</sup></i> is designed to be an accessible guide to quantum theory and its applications. The textbook uses the popular MATLAB<i><sup>®</sup></i> software for the numerical solution of quantum mechanical problems, with a particular focus on clusters and assemblies of atoms. <p>The textbook is written by a noted researcher and expert on the topic who introduces density functional theory, variational calculus and other practice-proven methods for the solution of quantum-mechanical problems. This important guide: <ul> <li>Presents the material in a didactical manner to help students grasp the concepts and applications of quantum theory</li> <li>Covers topics such as clusters, nanocrystals, transitions and organic molecules</li> <li>Offers MATLAB<i><sup>®</sup></i> codes to solve real-life quantum mechanical problems</li> </ul> <p>Written for master's and PhD students in physics, chemistry, material science, and engineering sciences, <i>Introductory Quantum Mechanics with MATLAB<sup>®</sup></i> contains an accessible approach to understanding the concepts of quantum theory applied to atoms, clusters, and crystals.

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