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Introductory Quantum Mechanics with MATLAB PDF Book

Introductory Quantum Mechanics with MATLAB: PDF Book writing by James R. Chelikowsky for free Download.
Presents a unique approach to grasping the concepts of quantum theory with a focus on atoms, clusters, and crystals

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.

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:

-Presents the material in a didactical manner to help students grasp the concepts and applications of quantum theory

-Covers a wealth of cutting-edge topics such as clusters, nanocrystals, transitions and organic molecules

-Offers MATLAB codes to solve real-life quantum mechanical problems

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.

Contents

Preface xi

1 Introduction 

1.1 Different Is Usually Controversial 

1.2 The Plan: Addressing Dirac’s Challenge 

Reference 

2 The Hydrogen Atom 

2.1 The Bohr Model 

2.2 The Schrödinger Equation 

2.3 The Electronic Structure of Atoms and the Periodic Table 

References 

3 Many-electron Atoms 

3.1 The Variational Principle 

3.1.1 Estimating the Energy of a Helium Atom 

3.2 The Hartree Approximation 

3.3 The Hartree–Fock Approximation 

References 

4 The Free Electron Gas 

4.1 Free Electrons 

4.2 Hartree–Fock Exchange in a Free Electron Gas 

References 

5 Density Functional Theory 

5.1 Thomas–Fermi Theory 

5.2 The Kohn–Sham Equation 

References 

6 Pseudopotential Theory 

6.1 The Pseudopotential Approximation 

6.1.1 Phillips–Kleinman Cancellation Theorem 

6.2 Pseudopotentials Within Density Functional Theory 

References 

7 Methods for Atoms 

7.1 The Variational Approach 

7.1.1 Estimating the Energy of the Helium Atom. 

7.2 Direct Integration 

7.2.1 Many-electron Atoms Using Density Functional Theory 

References 

8 Methods for Molecules, Clusters, and Nanocrystals 

8.1 The H2 Molecule: Heitler–London Theory 

8.2 General Basis 

8.2.1 Plane Wave Basis 

8.2.2 Plane Waves Applied to Localized Systems 

8.3 Solving the Eigenvalue Problem 

8.3.1 An Example Using the Power Method References 

9 Engineering Quantum Mechanics 

9.1 Computational Considerations 

9.2 Finite Difference Methods 

9.2.1 Special Diagonalization Methods: Subspace Filtering  References 

10 Atoms 

10.1 Energy levels 

10.2 Ionization Energies 

10.3 Hund’s Rules 

10.4 Excited State Energies and Optical Absorption 

10.5 Polarizability 

References 

11 Molecules

11.1 Interacting Atoms 

11.2 Molecular Orbitals: Simplified 

11.3 Molecular Orbitals: Not Simplified 

11.4 Total Energy of a Molecule from the Kohn–Sham Equations 

11.5 Optical Excitations 

11.5.1 Time-dependent Density Functional Theory 

11.6 Polarizability 

11.7 The Vibrational Stark Effect in Molecules 

References 

12 Atomic Clusters 

12.1 Defining a Cluster 

12.2 The Structure of a Cluster 

12.2.1 Using Simulated Annealing for Structural Properties 

12.2.2 Genetic Algorithms 

12.2.3 Other Methods for Determining Structural Properties 

12.3 Electronic Properties of a Cluster 

12.3.1 The Electronic Polarizability of Clusters 

12.3.2 The Optical Properties of Clusters 

12.4 The Role of Temperature on Excited-state Properties 

12.4.1 Magnetic Clusters of Iron 

References 

13 Nanocrystals 

13.1 Semiconductor Nanocrystals: Silicon 

13.1.1 Intrinsic Properties 

13.1.1.1 Electronic Properties 

13.1.1.2 Effective Mass Theory 

13.1.1.3 Vibrational Properties 

13.1.1.4 Example of Vibrational Modes for Si Nanocrystals 

13.1.2 Extrinsic Properties of Silicon Nanocrystals 

13.1.2.1 Example of Phosphorus-Doped Silicon Nanocrystals 

About the book:

Year:  2019
Publisher:  Wiley-VCH
Language:  English
Pages: 224
File:  PDF, 5.34 MB
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