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Solid state and quantum theory for optoelectronics
1 online resource (xix, 828 pages) : illustrations
"While applications rapidly change from one to the next in our commercialized world, the fundamental principles behind those applications remain constant. So if one understands those principles well enough and has ample experience in applying them, he or she will be able to develop a capacity for reaching results via conceptual thinking rather than having to always rely on models to test various conditions." "In Solid State and Quantum Theory for Optoelectronics, Michael Parker provides a general conceptual framework for matter that leads to the matter-light interaction explored in the author's Physics of Optoelectronics. Instead of overburdening readers with the definition-theorem-proof format often expected in mathematics texts, this book instructs readers through the development of conceptual pictures."--Jacket.
Chapter 1 Introduction to the Solid State; 1.1 Brief Preview; 1.2 Introduction to Matter and Bonds; 1.2.1 Gasses and Liquids; 1.2.2 Solids; 1.2.3 Bonding and the Periodic Table; 1.2.4 Dopant Atoms; 1.3 Introduction to Bands and Transitions; 1.3.1 Intuitive Origin of Bands; 1.3.2 Indirect Bands and Light- and Heavy-Hole Bands; 1.3.3 Introduction to Transitions; 1.3.4 Introduction to Band-Edge Diagrams; 1.3.5 Bandgap States and Defects; 1.4 Introduction to the pn Junction; 1.4.1 Junction Technology; 1.4.2 Band-Edge Diagrams and the pn Junction; 1.4.3 Nonequilibrium Statistics; 1.5 Device Trends; 1.5.1 Monolithic Integration of Device Types; 1.5.2 Year 2000 Benchmarks; 1.5.3 Small Optical Signals; 1.5.4 Fabrication Challenges; 1.6 Vacuum Tubes and Transistors; 1.6.1 Vacuum Tube; 1.6.2 Bipolar Transistor; 1.6.3 Field-Effect Transistor; 1.7 Brief Summary of Some Early Nanometer-Scale Devices
; 1.7.1 Resonant-Tunnel Device; 1.7.2 Resonant-Tunneling Transistor; 1.7.2.1 Single-Electron Transistors; 1.7.2.2 Quantum Cellular Automation (QCA); 1.7.2.3 Aharanov-Bohm Effect Device; 1.7.2.4 Quantum Interference Devices; 1.7.2.5 Josephson Junction; 1.8 Review Exercises; References and Further Readings; Chapter 2 Vector and Hilbert Spaces; 2.1 Vector and Hilbert Spaces; 2.1.1 Motivation for Linear Algebra in Quantum Theory; 2.1.2 Definition of Vector Space; 2.1.3 Hilbert Space; 2.1.4 Comment on the Length of a Vector for Quantum Theory; 2.1.5 Linear Isomorphism; 2.1.6 Antilinear Isomorphism; 2.2 Dirac Notation and Euclidean Vector Spaces; 2.2.1 Kets, Bras,
And Brackets for Euclidean Space; 2.2.2 Basis and Completeness for Euclidean Space; 2.2.3 Closure Relation for the Euclidean Vector Space; 2.2.4 Euclidean Dual Vector Space; 2.2.5 Inner Product and Norm; 2.3 Introduction to Coordinate and Vector Representation of Functions; 2.3.1 Initial View of the Coordinate Representation of Functions; 2.3.2 Coordinate Basis Set; 2.3.3 Introduction to the Inner Product for Functions; 2.3.4 Representations of Functions; 2.4 Function Space with Discrete Basis Sets; 2.4.1 Introduction to Hilbert Space; 2.4.2 Hilbert Space of Functions with Discrete Basis Vectors; 2.4.3 Closure Relation for Functions with a Discrete Basis; 2.4.4 Norms and Inner Products for Function Spaces with Discrete Basis Sets; 2.4.5 Discussion of Weight Functions; 2.4.6 Some Miscellaneous Notes on Notation; 2.5 Function Spaces with Continuous Basis Sets; 2.5.1 Continuous Basis Set of Functions; 2.5.2 Coordinate Space; 2.5.3
Representations of the Dirac Delta Using Basis Vectors; 2.6 Graham-Schmidt Orthonormalization Procedure; 2.6.1 Simplest Case of Two Vectors; 2.6.2 More than Two Vectors; 2.7 Fourier Basis Sets; 2.7.1 Fourier Cosine Series; 2.7.2 Fourier Sine Series; 2.7.3 Fourier Series; 2.7.4 Alternate Basis for the Fourier Series; 2.7.5 Fourier Transform; 2.8 Closure Relations, Kronecker Delta,
And Dirac Delta Functions; 2.8.1 Alternate Closure Relations and Representations of the Kronecker Delta Function for Euclidean Space; 2.8.2 Cosine Basis Functions; 2.8.3 Sine Basis Functions; 2.8.4 Fourier Series Basis Functions; 2.8.5 Some Notes; 2.9 Introduction to Direct Product Spaces; 2.9.1 Overview of Direct Product Spaces; 2.9.2 Introduction to Dyadic Notation for the Tensor Product of Two Euclidean Vectors; 2.9.3 Direct Product Space from the Fourier Series; 2.9.4 Components and Closure Relation for the Direct Product of Functions with Discrete Basis Sets; 2.9.5 Notes on the Direct Products of Continuous Basis Sets; 2.10 Introduction to Minkowski Space; 2.10.1 Coordinates and Pseudo-Inner Product; 2.10.2 Pseudo-Orthogonal Vector Notation; 2.10.3 Tensor Notation; 2.10.4 Derivatives; 2.11 Brief Discussion of Probability and Vector Components; 2.11.1 Simple 2-D Space for Starters; 2.11.2 Introduction to Applications of the
Probability; 2.11.3 Discrete and Continuous Hilbert Spaces; 2.11.4 Contrast with Random Vectors; 2.12 Review Exercises; References and Further Readings; Chapter 3 Operators and Hilbert Space; 3.1 Introduction to Operators and Groups; 3.1.1 Linear Operator; 3.1.2 Transformations of the Basis Vectors Determine the Linear Operator; 3.1.3 Introduction to Isomorphisms; 3.1.4 Comments on Groups and Operators; 3.1.5 Permutation Group and a Matrix Representation: An Example; 3.2 Matrix Representations; 3.2.1 Definition of Matrix for an Operator with Identical Domain and Range Spaces; 3.2.2 Matrix of an Operator with Distinct Domain and Range Spaces; 3.2.3 Dirac Notation for Matrices; 3.2.4 Operating on an Arbitrary Vector; 3.2.5 Matrix Equation; 3.2.6 Matrices for Function Spaces; 3.2.7 Introduction to Operator Expectation Values; 3.2.8 Matrix Notation for Averages; 3.3 Common Matrix Operations; 3.3.1 Composition of
Operators; 3.3.2 Isomorphism between Operators and Matrices; 3.3.3 Determinant; 3.3.4 Introduction to the Inverse of an Operator; 3.3.5 Trace; 3.3.6 Transpose and Hermitian Conjugate of a Matrix; 3.4 Operator Space; 3.4.1 Concepts and Section Summary; 3.4.2 Basis Expansion of a Linear Operator; 3.4.3 Introduction to the Inner Product for a Hilbert Space of Operators; 3.4.4 Proof of the Inner Product; 3.4.5 Basis for Matrices; 3.5 Operators and Matrices in Direct Product Space; 3.5.1 Review of Direct Product Spaces; 3.5.2 Operators; 3.5.3 Matrices of Direct Product Operators; 3.5.4 Matrix Representation of Basis Vectors for Direct Product Space; 3.6 Commutators and Algebra of Operators; 3.6.1 Initial Discussion of Operator Algebra; 3.6.2 Introduction to Commutators; 3.6.3 Some Commutator Theorems; 3.7 Unitary Operators and Similarity Transformations; 3.7.1 Orthogonal Rotation Matrices; 3.7.2 Unitary Transformations; 3.7.3
Visualizing Unitary Transformations; 3.7.4 Trace and Determinant; 3.7.5 Similarity Transformations; 3.7.6 Equivalent and Reducible Representations of Groups; 3.8 Hermitian Operators and the Eigenvector Equation; 3.8.1 Adjoint, Self-Adjoint, and Hermitian Operators; 3.8.2 Adjoint and Self-Adjoint Matrices; 3.9 Relation between Unitary and Hermitian Operators; 3.9.1 Relation between Hermitian and Unitary Operators; 3.10 Eigenvectors and Eigenvalues for Hermitian Operators; 3.10.1 Basic Theorems for Hermitian Operators; 3.10.2 Direct Product Space; 3.11 Eigenvectors, Eigenvalues,
And Diagonal Matrices; 3.11.1 Motivation for Diagonal Matrices; 3.11.2 Eigenvectors and Eigenvalues; 3.11.3 Diagonalize a Matrix; 3.11.4 Relation between a Diagonal Operator and the Change-of-Basis Operator; 3.12 Theorems for Hermitian Operators; 3.12.1 Common Theorems; 3.12.2 Bounded Hermitian Operators Have Complete Sets of Eigenvectors; 3.12.3 Derivation of the Heisenberg Uncertainty Relation; 3.13 Raising-Lowering and Creation-Annihilation Operators; 3.13.1 Definition of the Ladder Operators; 3.13.2 Matrix and Basis-Vector Representations of the Raising and Lowering Operators; 3.13.3 Raising and Lowering Operators for Direct Product Space; 3.14 Translation Operators; 3.14.1 Exponential Form of the Translation Operator; 3.14.2 Translation of the Position Operator; 3.14.3 Translation of the Position-Coordinate Ket; 3.14.4 Example Using the Dirac Delta Function; 3.14.5 Relation among Hilbert Space and the 1-D Translation,
And Lie Group; 3.14.6 Translation Operators in Three Dimensions; 3.15 Functions in Rotated Coordinates; 3.15.1 Rotating Functions; 3.15.2 Rotation Operator; 3.15.3 Rectangular Coordinates for the Generator of Rotations about z; 3.15.4 Rotation of the Position Operator; 3.15.5 Structure Constants and Lie Groups; 3.15.6 Structure Constants for the Rotation Lie Group; 3.16 Dyadic Notation; 3.16.1 Notation; 3.16.2 Equivalence between the Dyad and the Matrix; 3.17 Review Exercises; References and Further Reading; Chapter 4 Fundamentals of Classical Mechanics; 4.1 Constraints and Generalized Coordinates; 4.1.1 Constraints; 4.1.2 Generalized Coordinates; 4.1.3 Phase Space Coordinates; 4.2 Action, Lagrangian,
And Lagrange's Equation; 4.2.1 Origin of the Lagrangian in Newton's Equations; 4.2.2 Lagrange's Equation from a Variational Principle; 4.3 Hamiltonian; 4.3.1 Hamiltonian from the Lagrangian; 4.3.2 Hamilton's Canonical Equations; 4.4 Poisson Brackets
Includes bibliographical references and index.