Solid state and quantum theory for optoelectronics. (©2010)

• Record Type: Book
• Further Information: Note: Michael A. Parker.
• Other Names: Parker, Michael A
• Contents: 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<BR
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2010
• Copyright Date: 2010
• Extent: 1 online resource (xix, 828 pages), illustrations
• Subjects: 621.381/045; Optoelectronics; Quantum theory; Solid state physics; TECHNOLOGY & ENGINEERING -- Electronics -- Optoelectronics; Optoelectronics; Quantum theory; Solid state physics; Optoelektronik; Kvantteori; Fasta tillståndets fysik; Electronic books
• Languages: English
• ISBNs: 9781420019452; 1420019457
• Related ISBNs: 9780849337505
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.