APPLIED QUANTUM MECHANICS
CONTENTS INTRODUCTION MOTIVATION CLASSICAL MECHANICS THE ONE-DIMENSIONAL SIMPLE HARMONIC OSCILLATOR HARMONIC OSCILLATION OF A DIATOMIC MOLECULE THE MONATOMIC LINEAR CHAIN THE DIATOMIC LINEAR CHAIN CLASSICAL ELECTROMAGNETISM ELECTROSTATICS ELECTRODYNAMICS EXAMPLE EXERCISES PROBLEMS TOWARD QUANTUM MECHANICS DIFFRACTION AND INTERFERENCE OF LIGHT BLACK-BODY RADIATION AND EVIDENCE FOR QUANTIZATION OF LIGHT PHOTOELECTRIC EFFECT AND THE PHOTON PARTICLE SECURE QUANTUM COMMUNICATION THE LINK BETWEEN QUANTIZATION OF PHOTONS AND OTHER PARTICLES DIFFRACTION AND INTERFERENCE OF ELECTRONS WHEN IS A PARTICLE A WAVE? THE SCHRÖDINGER WAVE EQUATION THE WAVE FUNCTION DESCRIPTION OF AN ELECTRON IN FREE SPACE THE ELECTRON WAVE PACKET AND DISPERSION THE HYDROGEN ATOM PERIODIC TABLE OF ELEMENTS CRYSTAL STRUCTURE ELECTRONIC PROPERTIES OF BULK SEMICONDUCTORS AND HETEROSTRUCTURES USING THE SCHRÖDINGER WAVE EQUATION THE EFFECT OF DISCONTINUITY IN THE WAVE FUNCTION AND ITS SLOPE WAVE FUNCTION NORMALIZATION AND COMPLETENESS INVERSION SYMMETRY IN THE POTENTIAL ONE-DIMENSIONAL RECTANGULAR POTENTIAL WELL WITH INFINITE BARRIER ENERGY NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION CURRENT FLOW CURRENT IN A RECTANGULAR POTENTIAL WELL WITH INFINITE BARRIER ENERGY CURRENT FLOW DUE TO A TRAVELING WAVE DEGENERACY AS A CONSEQUENCE OF SYMMETRY BOUND STATES IN THREE DIMENSIONS AND DEGENERACY OF EIGENVALUES SYMMETRIC FINITE-BARRIER POTENTIAL CALCULATION OF BOUND STATES IN A SYMMETRIC FINITE-BARRIER POTENTIAL TRANSMISSION AND REFLECTION OF UNBOUND STATES PROBABILITY CURRENT DENSITY FOR SCATTERING AT A STEP IMPEDANCE MATCHING FOR UNITY TRANSMISSION ACROSS A POTENTIAL STEP PARTICLE TUNNELING ELECTRON TUNNELING LIMIT TO REDUCTION IN SIZE OF CMOS TRANSISTORS THE NONEQUILIBRIUM ELECTRON TRANSISTOR ELECTRON PROPAGATION THE PROPAGATION MATRIX METHOD PROGRAM TO CALCULATE TRANSMISSION PROBABILITY TIME-REVERSAL SYMMETRY CURRENT CONSERVATION AND THE PROPAGATION MATRIX THE RECTANGULAR POTENTIAL BARRIER TRANSMISSION PROBABILITY FOR A RECTANGULAR POTENTIAL BARRIER TRANSMISSION AS A FUNCTION OF ENERGY TRANSMISSION RESONANCES RESONANT TUNNELING HETEROSTRUCTURE BIPOLAR TRANSISTOR WITH RESONANT TUNNEL-BARRIER RESONANT TUNNELING BETWEEN TWO QUANTUM WELLS THE POTENTIAL BARRIER IN THE DELTA FUNCTION LIMIT ENERGY BANDS IN A PERIODIC POTENTIAL BLOCH’S THEOREM THE PROPAGATION MATRIX APPLIED TO A PERIODIC POTENTIAL THE TIGHT BINDING APPROXIMATION CRYSTAL MOMENTUM AND EFFECTIVE ELECTRON MASS OTHER ENGINEERING APPLICATIONS THE WKB APPROXIMATION TUNNELING THROUGH A HIGH-ENERGY BARRIER OF FINITE WIDTH EIGENSTATES AND OPERATORS THE POSTULATES OF QUANTUM MECHANICS ONE-PARTICLE WAVE FUNCTION SPACE PROPERTIES OF LINEAR OPERATORS PRODUCT OF OPERATORS PROPERTIES OF HERMITIAN OPERATORS NORMALIZATION OF EIGENFUNCTIONS COMPLETENESS OF EIGENFUNCTIONS COMMUTATOR ALGEBRA DIRAC NOTATION MEASUREMENT OF REAL NUMBERS EXPECTATION VALUE OF AN OPERATOR TIME DEPENDENCE OF EXPECTATION VALUE UNCERTAINTY OF EXPECTATION VALUE THE GENERALIZED UNCERTAINTY RELATION THE NO CLONING THEOREM DENSITY OF STATES DENSITY OF ELECTRON STATES CALCULATING DENSITY OF STATES FROM A DISPERSION RELATION DENSITY OF PHOTON STATES THE HARMONIC OSCILLATOR THE HARMONIC OSCILLATOR POTENTIAL CREATION AND ANNIHILATION OPERATORS THE GROUND STATE OF THE HARMONIC OSCILLATOR EXCITED STATES OF THE HARMONIC OSCILLATOR AND NORMALIZATION OF EIGENSTATES THE HARMONIC OSCILLATOR WAVE FUNCTIONS THE CLASSICAL TURNING POINT OF THE HARMONIC OSCILLATOR TIME DEPENDENCE THE SUPERPOSITION OPERATOR MEASUREMENT OF A SUPERPOSITION STATE TIME DEPENDENCE OF CREATION AND ANNIHILATION OPERATORS QUANTIZATION OF ELECTROMAGNETIC FIELDS LASER LIGHT QUANTIZATION OF AN ELECTRICAL RESONATOR QUANTIZATION OF LATTICE VIBRATIONS QUANTIZATION OF MECHANICAL VIBRATIONS FERMIONS AND BOSONS THE SYMMETRY OF INDISTINGUISHABLE PARTICLES FERMI–DIRAC DISTRIBUTION AND CHEMICAL POTENTIAL WRITING A COMPUTER PROGRAM TO CALCULATE THE CHEMICAL POTENTIAL WRITING A COMPUTER PROGRAM TO PLOT THE FERMI–DIRAC DISTRIBUTION FERMI–DIRAC DISTRIBUTION FUNCTION AND THERMAL EQUILIBRIUM STATISTICS THE BOSE–EINSTEIN DISTRIBUTION FUNCTION TIME-DEPENDENT PERTURBATION AN ABRUPT CHANGE IN POTENTIAL TIME-DEPENDENT CHANGE IN POTENTIAL FIRST-ORDER TIME-DEPENDENT PERTURBATION CHARGED PARTICLE IN A HARMONIC POTENTIAL FERMI’S GOLDEN RULE ELASTIC SCATTERING FROM IONIZED IMPURITIES THE COULOMB POTENTIAL LINEAR SCREENING OF THE COULOMB POTENTIAL PHOTON EMISSION DUE TO ELECTRONIC TRANSITIONS DENSITY OF OPTICAL MODES IN THREE-DIMENSIONS LIGHT INTENSITY BACKGROUND PHOTON ENERGY DENSITY AT THERMAL EQUILIBRIUM FERMI’S GOLDEN RULE FOR STIMULATED OPTICAL TRANSITIONS THE EINSTEIN AND COEFFICIENTS THE SEMICONDUCTOR LASER SPONTANEOUS AND STIMULATED EMISSION ABSORPTION AND ITS RELATION TO SPONTANEOUS EMISSION OPTICAL TRANSITIONS USING FERMI’S GOLDEN RULE OPTICAL GAIN IN THE PRESENCE OF ELECTRON SCATTERING DESIGNING A LASER DIODE THE OPTICAL CAVITY MIRROR LOSS AND PHOTON LIFETIME THE FABRY–PEROT LASER DIODE SEMICONDUCTOR LASER DIODE RATE EQUATIONS NUMERICAL METHOD OF SOLVING RATE EQUATIONS THE RUNGE–KUTTA METHOD LARGE-SIGNAL TRANSIENT RESPONSE CAVITY FORMATION NOISE IN LASER DIODE LIGHT EMISSION WHY OUR MODEL WORKS TIME-INDEPENDENT PERTURBATION TIME-INDEPENDENT NONDEGENERATE PERTURBATION THE FIRST-ORDER CORRECTION THE SECOND-ORDER CORRECTION HARMONIC OSCILLATOR SUBJECT TO PERTURBING POTENTIAL IN X TIME-INDEPENDENT DEGENERATE PERTURBATION A TWO-FOLD DEGENERACY SPLIT BY TIME-INDEPENDENT PERTURBATION MATRIX METHOD THE TWO-DIMENSIONAL HARMONIC OSCILLATOR SUBJECT TO PERTURBATION IN XY PERTURBATION OF TWO-DIMENSIONAL POTENTIAL WITH INFINITE BARRIER ENERGY ANGULAR MOMENTUM AND THE HYDROGENIC ATOM ANGULAR MOMENTUM CLASSICAL ANGULAR MOMENTUM THE ANGULAR MOMENTUM OPERATOR GEOMETRICAL REPRESENTATION SPHERICAL COORDINATES AND SPHERICAL HARMONICS THE RIGID ROTATOR EIGENSTATES AND EIGENVALUES OF THE HYDROGEN ATOM HYDROGENIC ATOM WAVE FUNCTIONS ELECTROMAGNETIC RADIATION FINE STRUCTURE OF THE HYDROGEN ATOM AND ELECTRON SPIN HYBRIDIZATION BALL AND STICK MODEL OF A DNA MOLECULE ATOM TYPES ARE INDICATED PHOTOGRAPH (LEFT) OF THE FIRST TRANSISTOR BRATTAIN AND BARDEEN’S P-N-P POINT-CONTACT GERMANIUM TRAN- SISTOR OPERATED AS A SPEECH AMPLIFIER WITH A POWER GAIN OF 18 ON DECEMBER 23, 1947 THE DEVICE IS A FEW MM IN SIZE ON THE RIGHT IS A SCANNING CAPACITANCE MICROSCOPE CROSS-SECTION IMAGE OF A SILICON P-TYPE METAL-OXIDE- SEMICONDUCTOR FIELD-EFFECT TRANSISTOR (P-MOSFET) WITH AN EFFECTIVE CHANNEL LENGTH OF ABOUT 20 NM, OR ABOUT ATOMS 4 THIS IMAGE OF A SMALL TRANSISTOR WAS PUBLISHED IN 1998, 50 YEARS AFTER BRATTAIN AND BARDEEN’S DEVICE IMAGE COURTESY OF G TIMP, UNIVERSITY OF ILLINOIS 1 S WEISS, SCIENCE 283, 1676 (1999) 2 G E MOORE, ELECTRONICS 38, 114 (1965) ALSO REPRINTED IN PROC IEEE 86, 82 (1998) 3 HTTP://WWW SEMATECH ORG 4 ALSO SEE G TIMP ET AL IEEE INTERNATIONAL ELECTRON DEVICES MEETING (IEDM) TECHNICAL DIGEST P 615, DEC 6–9, SAN FRANCISCO, CALIFORNIA, 1998 (ISBN 078034779)