Quantum Mechanics :

Singh, Jasprit.

Quantum Mechanics : Fundamentals and Applications to Technology. - 1st ed. - 1 online resource (538 pages)

QUANTUM MECHANICS Fundamentals and Applications to Technology -- CONTENTS -- PREFACE -- INTRODUCTION -- QUANTUM MECHANICS AND TECHNOLOGY -- Some Technology Needs and Challenges -- GUIDELINES FOR THE INSTRUCTOR -- SOME IMPORTANT REFERENCES -- Historical Development of Quantum Mechanics -- Textbooks -- General -- 1 A JOLT FOR CLASSICAL PHYSICS -- 1.1 INTRODUCTION -- 1.1.1 A Bit of History -- 1.1.2 Some Simple Questions -- 1.2 SOME EXPERIMENTS THAT DEFIED CLASSICAL PHYSICS -- 1.3 A PREVIEW OF THE TRANSITION FROM CLASSICAL TO QUANTUM PHYSICS -- 1.3.1 Newtonian Mechanics -- 1.3.2 Classical Wave Phenomena -- 1.3.3 The Wave-Particle Duality: A Hint in Optics -- 1.4 MODERN CLASSICAL MECHANICS: A BRIEF OVERVIEW -- 1.4.1 The Lagrangian Equations -- 1.4.2 Hamilton Equations of Motion -- 1.4.3 The Poisson Bracket Description -- 1.4.4 The Hamilton-Jacobi Formulation -- 1.5 THE HAMILTON-JACOBI THEORY AND WAVE MECHANICS -- 1.6 CHAPTER SUMMARY -- 2 THE MATHEMATICAL FORMULATION OF QUANTUM MECHANICS -- 2.1 INTRODUCTION -- 2.1.1 What Are We Trying to Do? -- 2.2 THE SCHRÖDINGER EQUATION -- 2.3 THE WAVE AMPLITUDE -- 2.3.1 Normalization of the Wavefunction -- 2.3.2 The Probability Current Density -- 2.3.3 Expectation Values -- 2.4 WAVES, WAVEPACKETS AND UNCERTAINTY -- 2.4.1 Physical Observables and Commutation Relations -- 2.4.2 Properties of a Wavepacket: The Ehrenfest Theorem -- 2.5 HOW DOES ONE SOLVE THE SCHRÖDINGER EQUATION? -- 2.5.1 Time-Independent Hamiltonian Problem -- 2.5.2 Time-Dependent Hamiltonian -- 2.6 SOME MATHEMATICAL TOOLS FOR QUANTUM MECHANICS -- 2.6.1 Boundary Conditions on the Wavefunction -- 2.6.2 Basis Functions and the Eigenvalue Matrix -- 2.6.3 The Dirac δ-function -- 2.6.4 Dirac Notation: Bra and Ket -- 2.6.5 Important Representations in Quantum Mechanics -- 2.6.6 Hilbert Space -- 2.6.7 Hermitian and Unitary Matrices. 2.7 EQUATIONS OF MOTION -- 2.8 CHAPTER SUMMARY -- 2.9 PROBLEMS -- 3 PARTICLES IN SIMPLE POTENTIALS -- 3.1 INTRODUCTION -- 3.2 THE FREE PARTICLE PROBLEM AND DENSITY OF STATES -- 3.2.1 Density of States for a Three-Dimensional System -- 3.2.2 Density of States in Sub-Three-Dimensional Systems -- 3.3 PARTICLE IN A QUANTUM WELL -- 3.3.1 The Square Quantum Well -- 3.3.2 Particle in a Triangular Quantum Well -- 3.3.3 Particle in an Arbitrary Quantum Well -- 3.3.4 Application Example: Confined Levels in Semiconductor Transistors -- 3.4 PARTICLE IN A PERIODIC POTENTIAL: BLOCH THEOREM -- 3.4.1 The Kronig-Penney Model for Bandstructure -- 3.4.2 Significance of the k-Vector -- 3.5 THE HARMONIC OSCILLATOR -- 3.6 THE MATRIX FORMULATION OF THE HARMONIC OSCILLATOR -- 3.7 HARMONIC OSCILLATOR: QUANTUM AND CLASSICAL TREATMENT -- 3.8 CHAPTER SUMMARY -- 3.9 PROBLEMS -- 4 THE TUNNELING PROBLEM -- 4.1 INTRODUCTION -- 4.2 THE GENERAL TUNNELING PROBLEM -- 4.2.1 Approaches to the Tunneling Problem -- 4.3 STATIONARY STATE APPROACH TO TUNNELING -- 4.3.1 Tunneling through a Square Potential Barrier -- 4.3.2 Application Example: Ohmic Contacts -- 4.3.3 Application Example: Field Emission Devices -- 4.3.4 Application Example: Scanning Tunneling Microscopy -- 4.3.5 Application Example: Josephson Junction -- 4.4 TUNNELING THROUGH MULTIPLE BARRIERS: RESONANT TUNNELING -- 4.4.1 Application Example: Resonant Tunneling Diode -- 4.5 TIME-DEPENDENT APPROACH TO TUNNELING -- 4.5.1 Propagation of a Wavepacket -- 4.6 A NUMERICAL APPROACH TO WAVEPACKET EVOLUTION -- 4.7 QUASI-BOUND STATES AND TRANSMISSION RESONANCE WIDTHS -- 4.8 CHAPTER SUMMARY -- 4.9 PROBLEMS -- 5 PARTICLES IN SPHERICALLY SYMMETRIC POTENTIALS -- 5.1 INTRODUCTION -- 5.2 SPHERICALLY SYMMETRIC POTENTIAL: GENERAL SOLUTION -- 5.3 THE ONE-ELECTRON ATOM AND THE HYDROGEN ATOM PROBLEM. 5.3.1 Application Example: Doping of Semiconductors -- 5.3.2 Application Example: Excitons in Semiconductors -- 5.4 FROM THE HYDROGEN ATOM TO THE PERIODIC TABLE: A QUALITATIVE VIEW -- 5.5 PARTICLE IN A THREE-DIMENSIONAL SQUARE WELL -- 5.6 QUASI-BOUND STATES AND TUNNELING IN SPHERICALLY SYMMETRIC POTENTIALS: RADIOACTIVITY -- 5.7 CHAPTER SUMMARY -- 5.8 PROBLEMS -- 6 PHYSICAL SYMMETRIES AND CONSERVATION LAWS -- 6.1 INTRODUCTION -- 6.2 SYMMETRY AND CONSERVATION LAWS -- 6.3 SPATIAL TRANSLATION AND MOMENTUM CONSERVATION -- 6.4 TIME DISPLACEMENT SYMMETRY -- 6.5 ROTATION SYMMETRY AND ANGULAR MOMENTUM -- 6.6 ANGULAR MOMENTUM: EIGENVALUES AND EIGENFUNCTIONS -- 6.7 SPIN ANGULAR MOMENTUM -- 6.8 COMBINATION OF ANGULAR MOMENTUM STATES -- 6.8.1 Clebsch-Gordon or Wigner Coefficients -- 6.8.2 Application Example: Bandedge States in Optical Materials -- 6.9 CHAPTER SUMMARY -- 6.10 PROBLEMS -- 7 IDENTICAL PARTICLES AND SECOND QUANTIZATION -- 7.1 INTRODUCTION -- 7.2 A SIMPLE EXPERIMENT WITH IDENTICAL PARTICLES -- 7.3 THE N-IDENTICAL-PARTICLE STATE -- 7.4 EXCHANGE INTERACTION -- 7.4.1 Application Example: Binding Energy of the H2+ Molecule Ion -- 7.4.2 The Neutral Hydrogen Molecule: Para- and Ortho-Hydrogen -- 7.5 THE SECOND QUANTIZATION -- 7.5.1 A Continuous Elastic System: Second Quantization -- 7.6 QUANTIZATION OF THE ELECTROMAGNETIC FIELD -- 7.6.1 The Classical Electromagnetic FieId -- 7.6.2 Second Quantization of the Radiation Field -- 7.7 QUANTIZATION OF LAWICE VIBRATIONS: PHONONS -- 7.8 PLASMONS, MAGNONS AND POLARONS -- 7.8.1 Collective Electron Vibrations: Plasmons -- 7.8.2 Spin Waves: Magnons -- 7.8.3 Electron-Lattice Polarization Excitation: Polarons -- 7.9 QUANTIZATION OF THE SCHRÖDINGER WAVE EQUATION FOR ELECTRONS -- 7.10 CLASSICAL AND QUANTUM STATISTICS -- 7.10.1 Application Example: Metals, Insulators and Semiconductors. 7.10.2 Application Example: Normal and Superconducting States -- 7.10.3 Ordinary and Supeffluid Liquid Helium -- 7.11 CHAPTER SUMMAFLY -- 7.12 PROBLEMS -- 8 APPROXIMATION METHODS: TIME-INDEPENDENT PROBLEMS -- 8.1 INTRODUCTION -- 8.2 STATIONARY PERTURBATION THEORY -- 8.2.1 Non-degenerate Case -- 8.2.2 Degenerate Case -- 8.3 SOME APPLICATIONS OF PERTURBATION THEORY -- 8.3.1 Band Theory and Effective Masses -- 8.3.2 Van der Waals Interactions -- 8.4 VARIATIONAL METHOD -- 8.4.1 Application Example: Exciton in Quantum Wells -- 8.5 THE WKB APPROXIMATION -- 8.5.1 Application to the Tunneling Problem -- 8.5.2 Application to the Quantization Rules -- 8.6 RESONANT COUPLING IN DOUBLE WELLS -- 8.6.1 Application Examples: Ammonia Molecules and Organic Dyes -- 8.6.2 Application Example: Atomic Clock -- 8.7 CHAPTER SUMMARY -- 8.8 PROBLEMS -- 9 TIME-DEPENDENT PROBLEMS: APPROXIMATION METHODS -- 9.1 INTRODUCTION -- 9.2 TIME-DEPENDENT PERTURBATION THEORY -- 9.2.1 Harmonic Perturbation -- 9.2.2 Transition Probability for Continuous Spectra -- 9.2.3 Higher Order Perturbation Theory -- 9.3 APPLICATION EXAMPLE: ELECTRON-PHOTON INTERACTION -- 9.3.1 Interband Transitions in Bulk Semiconductors -- 9.3.2 Interband Transitions in Quantum Wells -- 9.4 APPLICATION EXAMPLE: ELECTRON-PHONON SCATTERING -- 9.5 APPLICATION EXAMPLE: INDIRECT INTERBAND TRANSITIONS -- 9.6 APPLICATION EXAMPLE: CHARGE INJECTION AND RADIATIVE RECOMBINATION -- 9.6.1 Phosphors and Fluorescence -- 9.7 SLOWLY VARYING HAMILTONIAN: ADIABATIC APPROXIMATION -- 9.7.1 Adiabatic Approximation and Electron-Phonon Interactions -- 9.8 SUDDEN APPROXIMATION -- 9.9 CHAPTER SUMMARY -- 9.10 PROBLEMS -- 10 COLLISIONS AND SCATTERING -- 10.1 INTRODUCTION -- 10.2 TWO-PARTICLE COLLISIONS: CENTER OF MASS AND LABORATORY COORDINATE DESCRIPTION -- 10.2.1 Scattering Cross Section. 10.2.2 Scattering Angles in Laboratory and Center-of-Mass Systems -- 10.3 SCATTERING AS A STATIONARY STATE PROBLEM -- 10.3.1 An Integral Equation for Scattering -- 10.3.2 Microscopic Reversibility and Optical Theorem -- 10.4 THE BORN APPROXIMATION -- 10.4.1 Validity of the Born Approximation -- 10.5 PARTIAL WAVE ANALYSIS -- 10.5.1 Calculation of the Phase Shifts -- 10.6 APPLICATION EXAMPLE: SCREENED COULOMBIC POTENTIAL SCATTERING -- 10.6.1 Scattering Rate and Macroscopic Transport Properties -- 10.6.2 Ionized Impurity Limited Mobility -- 10.7 APPLICATION EXAMPLE: ALLOY SCATTERING -- 10.8 APPLICATION EXAMPLE: INTERFACE ROUGHNESS SCATTERING -- 10.9 APPLICATION EXAMPLE: CARRIER-CARRIER SCATTERING -- 10.9.1 Electron-Hole Scattering -- 10.9.2 Electron-Electron Scattering -- 10.9.3 Auger Processes and Impact Ionization -- 10.10 CHAPTER SUMMARY -- 10.11 PROBLEMS -- 11 MAGNETIC EFFECTS -- 11.1 INTRODUCTION -- 11.2 CHARGED PARTICLES IN A MAGNETIC FIELD: GENERAL HAMILTONIAN -- 11.3 FREE ELECTRONS IN A MAGNETIC FIELD -- 11.4 THE AHARONOV-BOHM EFFECT -- 11.5 APPLICATION EXAMPLE : SUPERCONDUCTING DEVICES -- 11.6 THE QUANTUM HALL EFFECT -- 11.7 THE ZEEMAN EFFECT -- 11.8 SPIN-ORBIT COUPLING -- 11.9 DIAMAGNETIC AND PARAMAGNETIC EFECTS -- 11.9.1 Diamagnetic Effect -- 11.9.2 Paramagnetic Effect -- 11.9.3 Paramagnetism in the Conduction Electrons in Metals -- 11 9 4 Application Example: Cooling by Demagnetization -- 11.10 EXCHANGE INTERACTION: FERROMAGNETISM AND ANTIFERROMAGNETISM -- 11.10.1 Exchange Interaction and Ferromagnetism -- 11.10.2 Antiferromagnetic Ordering -- 11.10.3 Application Example: Magnetic Recording -- 11.11 MAGNETIC RESONANCE EFFECTS -- 11.11.1 Nuclear Magnetic Resonance -- 11.12 CHAPTER SUMMARY -- 11.13 PROBLEMS -- APPENDIX -- A MODERN CLASSICAL PHYSICS: A REVIEW -- A.1 LAGRANGIAN EQUATIONS -- A.2 HAMILTON EQUATIONS OF MOTION. A.3 THE HAMILTON-JACOBI FORMULATION.

Explore the relationship between quantum mechanics and information-age applications This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.

9783527618200


Quantum theory.;Physics.


Electronic books.

QC174.12 -- .S534 1997eb

530.1/2