QUANTUM PRINCIPLES Perspective and Principles Prelude to Quantum Mechanics Stern-Gerlach Experiment Idealized Stern-Gerlach Results Classical Model Attempts Wave Functions for Two Physical-Outcome Case Process Diagrams, Operators, and Completeness Further Properties of Operators/Modulation Operator Reformulation Operator Rotation Bra-Ket Notation/Basis States Transition Amplitudes Three-Magnet Setup Example-Coherence Hermitian Conjugation Unitary Operators A Very Special Operator Matrix Representations Matrix Wave Function Recovery Expectation Values Wrap Up Problems Free Particles in One Dimension Photoelectric Effect Compton Effect Uncertainty Relation for Photons Stability of Ground States Bohr Model Fourier Transform and Uncertainty Relations Schrodinger Equation Schrodinger Equation Example Dirac Delta Functions Wave Functions and Probability Probability Current Time Separable Solutions Completeness for Particle States Particle Operator Properties Operator Rules Time Evolution and Expectation Values Wrap-Up Problems Some One-Dimensional Solutions to the Schrodinger Equation Introduction The Infinite Square Well: Differential Solution The Infinite Square Well: Operator Solution The Finite Potential Barrier Step Potential The Harmonic Oscillator The Attractive Kronig-Penny Model Bound State and Scattering Solutions Problems Hilbert Space and Unitary Transformations Introduction and Notation Inner and Outer Operator Products Operator-Matrix Relationship Hermitian Operators and Eigenkets Gram-Schmidt Orthogonalization Process Compatible Operators Uncertainty Relations and Incompatible Operators Simultaneously Measureable Operators Unitary Transformations and Change of Basis Coordinate Displacements and Unitary Transformations Schrodinger and Heisenburg Pictures of Time Evolution Free Gaussian Wave Packet in the Heisenberg Picture Potentials and the Ehrenfest Theorem Problems Three Static Approximation Methods Introduction Time-Independent Perturbation Theory Examples of Time-Independent Perturbation Theory Aspects of Degenerate Perturbation Theory WKB Semiclassical Approximation Use of the WKB Approximation in Barrier Penetration Use of the WKB Approximation in Bound States Variational Methods Problems Generalization to Three Dimensions Cartesian Basis States and Wave Functions in Three Dimensions Position/Momentum Eigenket Generalization Example: Three-Dimensional Infinite Square Well Spherical Basis States Orbital Angular Momentum Operator Effect of Angular Momentum on Basis States Energy Eigenvalue Equation and Angular Momentum Complete Set of Observables for the Radial Schrodinger Equation Specification of Angular Momentum Eigenstates Angular Momentum Eigenvectors and Spherical Harmonics Completeness and Other Properties of Spherical Harmonics Radial Eigenfunctions Problems QUANTUM PARTICLES The Three-Dimensional Radial Equation Recap of the Situation The Free Particle The Infinite Spherical Well Potential The Deuteron The Coulomb Potential: Initial Considerations The Coulomb Potential: 2-D Harmonic Oscillator Comparison The Confined Coulombic Model Problems Addition of Angular Momenta General Angular-Momentum Eigenstate Properties Combining Angular Momenta for Two Systems Explicit Example of Adding Two Spin 1/2 Systems Explicit Example of Adding Orbital Angular Momentum and Spin 1/2 Hydrogen Atom and the Choice of Basis States Hydrogen Atom and Perturbative Energy Shifts Problems Spin and Statistics The Connection between Spin and Statistics Building Wave Functions with Identical Particles Particle Occupation Basis More on Fermi-Dirac Statistics Interaction Operator and Feynman Diagrams Implications of Detailed Balance Cubical Enclosures and Particle States Maxwell-Boltzmann Statistics Bose-Einstein Statistics Fermi-Dirac Statistics The Hartree-Fock Equations Problems Quantum Particle Scattering Introduction The One-Dimensional Integral Schrodinger Equation Reflection and Transmission Amplitudes One-Dimensional Delta-Function Scattering Step-Function Potential Scattering The Born Series The Three-Dimensional Integral Schrodinger Equation The Helmholtz Equation and Plane Waves Cross Sections and the Scattering Amplitude Scattering Phase Shifts Finite-Range Potential Scattering The Three-Dimensional Born Series Identical Particle Scattering Proton-Proton Scattering Problems Connecting to the Standard Model Introduction Discrete Symmetries Parity Time Reversal Charge Conjugation Particle Primer Particle Interactions Quantum Electrodynamics Quantum Chromodynamics Weak Interactions Beyond the Standard Model Supersymmetry Superstrings Postlude Helpful Introductory Books on Particle and String Physics More Advanced Books on Particle and String Physics Problems Appendix: Notation Comments and Comparisons Appendix: Lattice Models Appendix: 2-D Harmonic Oscillator Wave Function Normalization Appendix: Allowed Standard Model Interactions Appendix: Weak Flavor Mixing Appendix: The Ising Model and More Index
QUANTUM PRINCIPLES Perspective and Principles Prelude to Quantum Mechanics Stern-Gerlach Experiment Idealized Stern-Gerlach Results Classical Model Attempts Wave Functions for Two Physical-Outcome Case Process Diagrams, Operators, and Completeness Further Properties of Operators/Modulation Operator Reformulation Operator Rotation Bra-Ket Notation/Basis States Transition Amplitudes Three-Magnet Setup Example-Coherence Hermitian Conjugation Unitary Operators A Very Special Operator Matrix Representations Matrix Wave Function Recovery Expectation Values Wrap Up Problems Free Particles in One Dimension Photoelectric Effect Compton Effect Uncertainty Relation for Photons Stability of Ground States Bohr Model Fourier Transform and Uncertainty Relations Schrodinger Equation Schrodinger Equation Example Dirac Delta Functions Wave Functions and Probability Probability Current Time Separable Solutions Completeness for Particle States Particle Operator Properties Operator Rules Time Evolution and Expectation Values Wrap-Up Problems Some One-Dimensional Solutions to the Schrodinger Equation Introduction The Infinite Square Well: Differential Solution The Infinite Square Well: Operator Solution The Finite Potential Barrier Step Potential The Harmonic Oscillator The Attractive Kronig-Penny Model Bound State and Scattering Solutions Problems Hilbert Space and Unitary Transformations Introduction and Notation Inner and Outer Operator Products Operator-Matrix Relationship Hermitian Operators and Eigenkets Gram-Schmidt Orthogonalization Process Compatible Operators Uncertainty Relations and Incompatible Operators Simultaneously Measureable Operators Unitary Transformations and Change of Basis Coordinate Displacements and Unitary Transformations Schrodinger and Heisenburg Pictures of Time Evolution Free Gaussian Wave Packet in the Heisenberg Picture Potentials and the Ehrenfest Theorem Problems Three Static Approximation Methods Introduction Time-Independent Perturbation Theory Examples of Time-Independent Perturbation Theory Aspects of Degenerate Perturbation Theory WKB Semiclassical Approximation Use of the WKB Approximation in Barrier Penetration Use of the WKB Approximation in Bound States Variational Methods Problems Generalization to Three Dimensions Cartesian Basis States and Wave Functions in Three Dimensions Position/Momentum Eigenket Generalization Example: Three-Dimensional Infinite Square Well Spherical Basis States Orbital Angular Momentum Operator Effect of Angular Momentum on Basis States Energy Eigenvalue Equation and Angular Momentum Complete Set of Observables for the Radial Schrodinger Equation Specification of Angular Momentum Eigenstates Angular Momentum Eigenvectors and Spherical Harmonics Completeness and Other Properties of Spherical Harmonics Radial Eigenfunctions Problems QUANTUM PARTICLES The Three-Dimensional Radial Equation Recap of the Situation The Free Particle The Infinite Spherical Well Potential The Deuteron The Coulomb Potential: Initial Considerations The Coulomb Potential: 2-D Harmonic Oscillator Comparison The Confined Coulombic Model Problems Addition of Angular Momenta General Angular-Momentum Eigenstate Properties Combining Angular Momenta for Two Systems Explicit Example of Adding Two Spin 1/2 Systems Explicit Example of Adding Orbital Angular Momentum and Spin 1/2 Hydrogen Atom and the Choice of Basis States Hydrogen Atom and Perturbative Energy Shifts Problems Spin and Statistics The Connection between Spin and Statistics Building Wave Functions with Identical Particles Particle Occupation Basis More on Fermi-Dirac Statistics Interaction Operator and Feynman Diagrams Implications of Detailed Balance Cubical Enclosures and Particle States Maxwell-Boltzmann Statistics Bose-Einstein Statistics Fermi-Dirac Statistics The Hartree-Fock Equations Problems Quantum Particle Scattering Introduction The One-Dimensional Integral Schrodinger Equation Reflection and Transmission Amplitudes One-Dimensional Delta-Function Scattering Step-Function Potential Scattering The Born Series The Three-Dimensional Integral Schrodinger Equation The Helmholtz Equation and Plane Waves Cross Sections and the Scattering Amplitude Scattering Phase Shifts Finite-Range Potential Scattering The Three-Dimensional Born Series Identical Particle Scattering Proton-Proton Scattering Problems Connecting to the Standard Model Introduction Discrete Symmetries Parity Time Reversal Charge Conjugation Particle Primer Particle Interactions Quantum Electrodynamics Quantum Chromodynamics Weak Interactions Beyond the Standard Model Supersymmetry Superstrings Postlude Helpful Introductory Books on Particle and String Physics More Advanced Books on Particle and String Physics Problems Appendix: Notation Comments and Comparisons Appendix: Lattice Models Appendix: 2-D Harmonic Oscillator Wave Function Normalization Appendix: Allowed Standard Model Interactions Appendix: Weak Flavor Mixing Appendix: The Ising Model and More Index
BRIEF REVIEW OF CLASSICAL THEORIES Harmonic Oscillator Boltzmann Transport Equation Maxwell's Equations MILESTONE DISCOVERIES AND OLD QUANTUM THEORY Blackbody Radiation and Quantum of Energy Specific Heat of Solids Photoelectric Effects Compton Scattering Duality of Matter Bohr?s H-Atom Theory SCHRODINGER EQUATION AND OPERATOR ALGEBRA Schrodinger Equation Momentum Eigenfunction and Fourier Series Hermitian Operator and Bra Ket Notations Orthgonality and Completeness of Eigenfunctions Basic Postulates of Quantum Mechanics Commutation Relations Conjugate Variables and Uncertainty Relation Operator Equation of Motion and Ehrenfest Theorem PARTICLE IN POTENTIAL WELL Infinite Square Well Potential Particle in 3-D Box Density of States: 1-D, 2-D and 3-D Particle in Quantum Well Particle in Delta Function Potential Well Quantum Well and Wire SCATTERING OF A PARTICLE AT 1-D POTENTIALS Scattering at Step Potential Scattering at Quantum Well TUNNELING AND ITS APPLICATIONS Tunneling across Square Potential Barrier Fowler-Nordheim and Direct Tunneling Resonant Tunneling The Applications of Tunneling PERIODIC POTENTIALS AND ENERGY BANDS 1-D Crystal and Kronig-Penny Model E-k Dispersion and Energy Bands Energy Bands and Resonant Tunneling THE HARMONIC OSCILLATOR Energy Eigenequation The Properties of Energy Eigenfunction The Operator Treatment THE ANGULAR MOMENTUM Angualr Momentum Operators Eigenfunctions and Spherical Harmonics THE HYDROGEN ATOM: THE SCHRODINGER TREATMENT Two-Body Central Force Problem The Hydrogen Atom The Atomic Orbital Virial Theorm and Doppler Shift SYSTEM OF IDENTICAL PARTICLES AND MANY-ELECTRON ATOMS Two Electron System Two Spin 1/2 System The Helium Atom The Periodic Table and the Structure of Atoms MOLECULES AND CHEMICAL BONDS The Ionized Hydrogen Molecule The Hydrogen Molecule Ionic Bond and Van der Waals Attraction THE PERTURBATION THEORY Time Independent Perturbation in Non-Degenerate Systems Time Dependent Perturbation Theory ATOM - FIELD INTERACTION Field Quantization Atom - Field Interaction Driven, Damped Two Level Atom INTERACTION BETWEEN EM WAVES AND OPTICAL MEDIA Attenuation and Dispersion of Waves Density Matrix and Ensemble Averaging Laser Devices QUANTUM STATISTICS General Background and Three Kinds of Particles Statistics for Distinguishable particles Statistics for Fermions and Fermi Distribution Function Statistics for Boson and Bose Einstein Distribution SEMICONDUCTOR STATISTICS Carrier Densities in Intrinsic Semiconductors Carrier Densities in Extrinsic Semiconductors Fermi Level in Extrinsic Semiconductors CHARGE TRANSPORT IN SEMICONDUCTORS Drift and Diffusion Currents Transport Coefficients Equilibrium and Non-Equilibrium Recombination and Generation Currents P-N JUNCTION DIODE The Junction Interface in Equilibrium The Junction Interface Under Bias The Diode I-V Applications of P-N Junction Diodes THE BIPOLAR JUNCTION TRANSISTOR: DEVICE PHYSICS AND TECHNOLOGY Bipolar Junction Transistor: Overview The Physics of Transistor Action Ebers Moll Equations Base Transit Time and Charge Control Model METAL OXIDE SILICON FIELD EFFECT TRANSISTORS (MOSFET) I: OVERVIEW OF DEVICE BEHAVIOR AND APPLICATIONS MOSFET: Overview Charge Control and Metal-Oxide-Silicon System NMOS I-V Applications of MOSFET METAL OXIDE SILICON FIELD EFFECT TRANSISTORS (MOSFET) II: DEVICE SCALING AND SCHOTTKY CONTACT Device Scaling: Physical issues and Limitations Metal - Semiconductor Contacts The I-V Behavior in Metal - Semiconductor Contacts
A Brief Survey of Analytical Dynamics, Discovery of Matrix Mechanics, Mathematical Preliminaries Postulates of Quantum Theory Equations of Motion, Hamiltonian Operator and the Commutation Relations Symmetries and Conservation Laws, Classical and Quantum Integrability Classical and Quantum Mechanical Degeneracies Bound State Energies for One-Dimensional Problems Exactly Solvable Potentials, Supersymmetry and Shape Invariance Supersymmetry and Superpotential Shape Invariant Potentials Two-Body Problem Determination of the Angular Momentum Eigenvalues Methods of Integration of the Heisenberg Equations of Motion Discrete-Time Formulation of the Heisenberg's Equations of Motion Quantum Tunneling Using Discrete-Time Formulation Integration of the Operator Differential Equations Perturbation Theory Other Methods of Approximation Heisenberg Correspondence Principle, Quantization of the Equations of Motion with Higher Derivatives Determinantal Method in Potential Scattering Time-Dependent Scattering Theory The Scattering Matrix Impact Parameter Representation of the Scattering Amplitude Transition Probability Quantum Diffraction, Motion of a Charged Particle in Electromagnetic Field The Aharanov-Bohm Effect Neutron Interferometry Quantum Many-Body Problem Hartree and Hartree-Fock Approximations Second Quantization Bogoliubov Transformation for a Many-Boson System Bogoliubov Transformation for Fermions Interacting Through Pairing Forces Quantum Theory of Free Electromagnetic Field Casimir Force Interaction of Radiation with Matter Heisenberg Equations for Interaction of an Atom with Radiation Bell's Inequalities
This textbook provides ample opportunities for practice and real experimental demonstrations. Conceptual understanding and mastering key techniques are enhanced by rigorous derivations, numerous worked examples, more than 300 exercises, about 150 problems and 16 computer codes. The preface summarizes all of the key concepts and formulas, along with a detailed schedule for teaching. The first three chapters introduce the quantum idea, wave-particle duality, operators and measurement. The Noether theorem is invoked to introduce the Schrödinger equation, followed by applications to infinite and finite quantum wells, quantum tunneling, harmonic oscillators, Heisenberg equation of motion, uncertainty principle, blackbody radiation and photoelectric effect. Chapters 4 and 5 are on angular momentum, the hydrogen atom and time-independent approximate methods. Chapters 6 and 7 are on spin and time-dependent perturbation theory. Chapters 8, 9 and 10 are on molecular orbitals, energy bands, quantum transport, scanning tunneling microscopy, lattice vibrations, Berry phase and quantum computing. The book is intended for a one-semester or one-year course and is also appropriate for researchers in related fields.
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
Assuming a background in basic classical physics, multivariable calculus, and differential equations, A Concise Introduction to Quantum Mechanics provides a self-contained presentation of the mathematics and physics of quantum mechanics. The relevant aspects of classical mechanics and electrodynamics are reviewed, and the basic concepts of wave-particle duality are developed as a logical outgrowth of experiments involving blackbody radiation, the photoelectric effect, and electron diffraction. The Copenhagen interpretation of the wave function and its relation to the particle probability density is presented in conjunction with Fourier analysis and its generalization to function spaces. These concepts are combined to analyze the system consisting of a particle confined to a box, developing the probabilistic interpretation of observations and their associated expectation values. The Schrödinger equation is then derived by using these results and demanding both Galilean invariance of the probability density and Newtonian energy-momentum relations. The general properties of the Schrödinger equation and its solutions are analyzed, and the theory of observables is developed along with the associated Heisenberg uncertainty principle. Basic applications of wave mechanics are made to free wave packet spreading, barrier penetration, the simple harmonic oscillator, the Hydrogen atom, and an electric charge in a uniform magnetic field. In addition, Dirac notation, elements of Hilbert space theory, operator techniques, and matrix algebra are presented and used to analyze coherent states, the linear potential, two state oscillations, and electron diffraction. Applications are made to photon and electron spin and the addition of angular momentum, and direct product multiparticle states are used to formulate both the Pauli exclusion principle and quantum decoherence. The book concludes with an introduction to the rotation group and the general properties of angular momentum.