Introductory Quantum Mechanics with MATLAB

James Chelikowsky, PhD, 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.

• Preface xi1 Introduction 11.1 Different Is Usually Controversial 11.2 The Plan: Addressing Dirac’s Challenge 2Reference 42 The Hydrogen Atom 52.1 The Bohr Model 52.2 The Schrödinger Equation 82.3 The Electronic Structure of Atoms and the Periodic Table 15References 183 Many-electron Atoms 193.1 The Variational Principle 193.1.1 Estimating the Energy of a Helium Atom 213.2 The Hartree Approximation 223.3 The Hartree–Fock Approximation 25References 274 The Free Electron Gas 294.1 Free Electrons 294.2 Hartree–Fock Exchange in a Free Electron Gas 35References 365 Density Functional Theory 375.1 Thomas–Fermi Theory 375.2 The Kohn–Sham Equation 40References 436 Pseudopotential Theory 456.1 The Pseudopotential Approximation 456.1.1 Phillips–Kleinman CancellationTheorem 476.2 PseudopotentialsWithin Density FunctionalTheory 50References 577 Methods for Atoms 597.1 The Variational Approach 597.1.1 Estimating the Energy of the Helium Atom. 597.2 Direct Integration 637.2.1 Many-electron Atoms Using Density FunctionalTheory 67References 698 Methods for Molecules, Clusters, and Nanocrystals 718.1 The H2 Molecule: Heitler–LondonTheory 718.2 General Basis 768.2.1 PlaneWave Basis 798.2.2 PlaneWaves Applied to Localized Systems 878.3 Solving the Eigenvalue Problem 898.3.1 An Example Using the Power Method 92References 959 Engineering Quantum Mechanics 979.1 Computational Considerations 979.2 Finite Difference Methods 999.2.1 Special DiagonalizationMethods: Subspace Filtering 101References 10410 Atoms 10710.1 Energy levels 10710.2 Ionization Energies 10810.3 Hund’s Rules 11010.4 Excited State Energies and Optical Absorption 11310.5 Polarizability 122References 12411 Molecules 12511.1 Interacting Atoms 12511.2 Molecular Orbitals: Simplified 12511.3 Molecular Orbitals: Not Simplified 13011.4 Total Energy of a Molecule from the Kohn–Sham Equations 13211.5 Optical Excitations 13711.5.1 Time-dependent Density FunctionalTheory 13811.6 Polarizability 14011.7 The Vibrational Stark Effect in Molecules 140References 15012 Atomic Clusters 15312.1 Defining a Cluster 15312.2 The Structure of a Cluster 15412.2.1 Using Simulated Annealing for Structural Properties 15512.2.2 Genetic Algorithms 15912.2.3 Other Methods for Determining Structural Properties 16212.3 Electronic Properties of a Cluster 16412.3.1 The Electronic Polarizability of Clusters 16412.3.2 The Optical Properties of Clusters 16612.4 The Role of Temperature on Excited-state Properties 16712.4.1 Magnetic Clusters of Iron 169References 17413 Nanocrystals 17713.1 Semiconductor Nanocrystals: Silicon 17913.1.1 Intrinsic Properties 17913.1.1.1 Electronic Properties 17913.1.1.2 Effective MassTheory 18413.1.1.3 Vibrational Properties 18713.1.1.4 Example of VibrationalModes for Si Nanocrystals 18813.1.2 Extrinsic Properties of Silicon Nanocrystals 19013.1.2.1 Example of Phosphorus-Doped Silicon Nanocrystals 191References 197A Units 199B A Working Electronic Structure Code 203References 206Index 207