The main topic of this book is quantum mechanics, as the title indicates. Itspecifically targets those topics within quantum mechanics that are needed tounderstand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at the heart of most electrical engineering theory. Inthis manner, the explanation of the quantum mechanics is rooted in the mathematics familiar to every electrical engineer. Secondly, beginning with the first chapter, simple computer programs in MATLAB are used to illustrate the principles. The programs can easily be copied and used by the reader to do the exercises at the end of the chapters or to just become more familiar with the material. INDICE: 1. Introduction 1.1 Why Quantum Mechanics 1.2 Simulation of the One-Dimensional, Time-Dependent Schrödinger Equation 1.3 Physical Parameters-theObservables 1.4 The Potential V(X) 1.5 Propagating Through Potential Barriers1.6 Summary 2. Stationary States 2.1 The Infinite Well 2.2 Eigenfunction Decomposition 2.3 Periodic Boundary Conditions 2.4 Eigenfunctions for Arbitrarily Shaped Potentials 2.5 Coupled Wells 2.6 Bra-ket Notation 2.7 Summary. 3. Fourier Theory in Quantum Mechanics 3.1 The Fourier Transform 3.2 Fourier Analysis and Available States 3.3 Uncertainty 3.4 Transmission via FFT 3.5 Summary 4. Matrix Algebra in Quantum Mechanics 4.1 Vector and Matrix Representation 4.2 Matrix Representation of the Hamiltonian 4.3 The Eigenspace Representation 4.4 Formalism 5. Statistical Mechanics 5.1 Density of States 5.2 Probability Distributions 5.3 The Equilibrium Distribution of Electrons and Holes 5.4 The Electron Density and the Density Matrix 6. Bands and Subbands 6.1 Bands in Semiconductors 6.2 The Effective Mass 6.3 Modes (Subbands) in Quantum Structures 7. TheSchrödinger Equation for Spin-1.2 Fermions 7.1 Spin in Fermions 7.2 An Electron in a Magnetic Field 7.3 A Charged Particle Moving in Combined E and B fields 7.4 The Hartree-Fock Approximation 8. Greens Functions Formulation 8.1 Introduction 8.2 The Density Matrix and the Spectral Matrix 8.3 The Matrix Version of the Greens Function 8.4 The Self-Energy Matrix 9. Transmission 9.1 The Single-Energy Channel 9.2 Current Flow 9.3 The Transmission Matrix 9.4 Conductance9.5 Büttiker probes 9.6 A Simulation Example 10. Approximation Methods 10.1 The Variational Method 10.2 Non-Degenerate Perturbation Theory 10.3 Degenerate Perturbation Theory 10.4 Time-Dependent Perturbation Theory 11. The Harmonic Oscillator 11.1 The Harmonic Oscillator in One Dimension 11.2 The Coherent State of the Harmonic Oscillator 11.3 The Two-Dimensional Harmonic Oscillator 12. Finding Eigenfunctions Using Time-Domain Simulation 12.1 Finding the Eigenenergies and Eigenfunctions in One-Dimension 12.2 Finding the Eigenfunctions of Two-Dimensional Structures 12.3 Finding a Complete set of Eigenfunctions Appendix A. Important Constants and Units Appendix B. Fourier Analysis and the Fast Fourier Transform (FFT) Appendix C. An Introduction to the Greens Function Appendix D. Listing of Computer Programs
- ISBN: 978-0-470-87409-7
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 448
- Fecha Publicación: 10/02/2012
- Nº Volúmenes: 1
- Idioma: Inglés