QUANTUM MECHANICS FOR SCIENTISTS AND ENGINEERS

By EMMA WHITE

CONTENTS CHAPTER INTRODUCTION QUANTUM MECHANICS AND REAL LIFE QUANTUM MECHANICS AS AN INTELLECTUAL ACHIEVEMENT USING QUANTUM MECHANICS CHAPTER WAVES AND QUANTUM MECHANICS – SCHRÖDINGER’S EQUATION RATIONALIZATION OF SCHRÖDINGER’S EQUATION PROBABILITY DENSITIES DIFFRACTION BY TWO SLITS LINEARITY OF QUANTUM MECHANICS: MULTIPLYING BY A CONSTANT NORMALIZATION OF THE WAVEFUNCTION PARTICLE IN AN INFINITELY DEEP POTENTIAL WELL (“PARTICLE IN A BOX”) PROPERTIES OF SETS OF EIGENFUNCTIONS PARTICLES AND BARRIERS OF FINITE HEIGHTS PARTICLE IN A FINITE POTENTIAL WELL HARMONIC OSCILLATOR PARTICLE IN A LINEARLY VARYING POTENTIAL SUMMARY OF CONCEPTS THE TIME-DEPENDENT SCHRÖDINGER EQUATION RATIONALIZATION OF THE TIME-DEPENDENT SCHRÖDINGER EQUATION RELATION TO THE TIME-INDEPENDENT SCHRÖDINGER EQUATION SOLUTIONS OF THE TIME-DEPENDENT SCHRÖDINGER EQUATION LINEARITY OF QUANTUM MECHANICS: LINEAR SUPERPOSITION TIME DEPENDENCE AND EXPANSION IN THE ENERGY EIGENSTATES TIME EVOLUTION OF INFINITE POTENTIAL WELL AND HARMONIC OSCILLATOR TIME EVOLUTION OF WAVEPACKETS QUANTUM MECHANICAL MEASUREMENT AND EXPECTATION VALUES THE HAMILTONIAN OPERATORS AND EXPECTATION VALUES TIME EVOLUTION AND THE HAMILTONIAN OPERATOR MOMENTUM AND POSITION OPERATORS UNCERTAINTY PRINCIPLE PARTICLE CURRENT QUANTUM MECHANICS AND SCHRÖDINGER’S EQUATION FUNCTIONS AND OPERATORS FUNCTIONS AS VECTORS VECTOR SPACE OPERATORS LINEAR OPERATORS EVALUATING THE ELEMENTS OF THE MATRIX ASSOCIATED WITH AN OPERATOR BILINEAR EXPANSION OF LINEAR OPERATORS SPECIFIC IMPORTANT TYPES OF LINEAR OPERATORS IDENTITY OPERATOR INVERSE OPERATOR UNITARY OPERATORS HERMITIAN OPERATORS MATRIX FORM OF DERIVATIVE OPERATORS MATRIX CORRESPONDING TO MULTIPLYING BY A FUNCTION OPERATORS AND QUANTUM MECHANICS COMMUTATION OF OPERATORS GENERAL FORM OF THE UNCERTAINTY PRINCIPLE TRANSITIONING FROM SUMS TO INTEGRALS CONTINUOUS EIGENVALUES AND DELTA FUNCTIONS APPROXIMATION METHODS IN QUANTUM MECHANICS EXAMPLE PROBLEM – POTENTIAL WELL WITH AN ELECTRIC FIELD USE OF FINITE MATRICES TIME-INDEPENDENT NON-DEGENERATE PERTURBATION THEORY DEGENERATE PERTURBATION THEORY TIGHT BINDING MODEL VARIATIONAL METHOD TIME-DEPENDENT PERTURBATION THEORY TIME-DEPENDENT PERTURBATIONS SIMPLE OSCILLATING PERTURBATIONS REFRACTIVE INDEX NONLINEAR OPTICAL COEFFICIENTS SUMMARY OF CONCEPTS QUANTUM MECHANICS IN CRYSTALLINE MATERIALS CRYSTALS ONE ELECTRON APPROXIMATION BLOCH THEOREM DENSITY OF STATES IN K-SPACE BAND STRUCTURE EFFECTIVE MASS THEORY DENSITY OF STATES IN ENERGY DENSITIES OF STATES IN QUANTUM WELLS K P METHOD USE OF FERMI’S GOLDEN RULE ANGULAR MOMENTUM ANGULAR MOMENTUM OPERATORS L SQUARED OPERATOR VISUALIZATION OF SPHERICAL HARMONIC FUNCTIONS COMMENTS ON NOTATION VISUALIZATION OF ANGULAR MOMENTUM CHAPTER 10 THE HYDROGEN ATOM MULTIPLE PARTICLE WAVEFUNCTIONS HAMILTONIAN FOR THE HYDROGEN ATOM PROBLEM COORDINATES FOR THE HYDROGEN ATOM PROBLEM SOLVING FOR THE INTERNAL STATES OF THE HYDROGEN ATOM SOLUTIONS OF THE HYDROGEN ATOM PROBLEM CHAPTER 11 METHODS FOR ONE-DIMENSIONAL PROBLEMS TUNNELING PROBABILITIES TRANSFER MATRIX PENETRATION FACTOR FOR SLOWLY VARYING BARRIERS ELECTRON EMISSION WITH A POTENTIAL BARRIER CHAPTER 12 SPIN ANGULAR MOMENTUM AND MAGNETIC MOMENTS STATE VECTORS FOR SPIN ANGULAR MOMENTUM OPERATORS FOR SPIN ANGULAR MOMENTUM THE BLOCH SPHERE DIRECT PRODUCT SPACES AND WAVEFUNCTIONS WITH SPIN PAULI EQUATION WHERE DOES SPIN COME FROM? CHAPTER 13 IDENTICAL PARTICLES SCATTERING OF IDENTICAL PARTICLES PAULI EXCLUSION PRINCIPLE STATES, SINGLE-PARTICLE STATES, AND MODES EXCHANGE ENERGY EXTENSION TO MORE THAN TWO IDENTICAL PARTICLES MULTIPLE PARTICLE BASIS FUNCTIONS THERMAL DISTRIBUTION FUNCTIONS IMPORTANT EXTREME EXAMPLES OF STATES OF MULTIPLE IDENTICAL PARTICLES QUANTUM MECHANICAL PARTICLES RECONSIDERED DISTINGUISHABLE AND INDISTINGUISHABLE PARTICLES CHAPTER 14 THE DENSITY MATRIX PURE AND MIXED STATES DENSITY OPERATOR DENSITY MATRIX AND ENSEMBLE AVERAGE VALUES TIME-EVOLUTION OF THE DENSITY MATRIX INTERACTION OF LIGHT WITH A TWO-LEVEL “ATOMIC” SYSTEM DENSITY MATRIX AND PERTURBATION THEORY CHAPTER 15 HARMONIC OSCILLATORS AND PHOTONS HARMONIC OSCILLATOR AND RAISING AND LOWERING OPERATORS HAMILTON’S EQUATIONS AND GENERALIZED POSITION AND MOMENTUM QUANTIZATION OF ELECTROMAGNETIC FIELDS NATURE OF THE QUANTUM MECHANICAL STATES OF AN ELECTROMAGNETIC MODE FIELD OPERATORS QUANTUM MECHANICAL STATES OF AN ELECTROMAGNETIC FIELD MODE GENERALIZATION TO SETS OF MODES VIBRATIONAL MODES CHAPTER 16 FERMION OPERATORS POSTULATION OF FERMION ANNIHILATION AND CREATION OPERATORS WAVEFUNCTION OPERATOR FERMION HAMILTONIANS CHAPTER 17 INTERACTION OF DIFFERENT KINDS OF PARTICLES STATES AND COMMUTATION RELATIONS FOR DIFFERENT KINDS OF PARTICLES OPERATORS FOR SYSTEMS WITH DIFFERENT KINDS OF PARTICLES PERTURBATION THEORY WITH ANNIHILATION AND CREATION OPERATORS STIMULATED EMISSION, SPONTANEOUS EMISSION, AND OPTICAL ABSORPTION CHAPTER 18 QUANTUM INFORMATION QUANTUM MECHANICAL MEASUREMENTS AND WAVEFUNCTION COLLAPSE QUANTUM CRYPTOGRAPHY ENTANGLEMENT QUANTUM COMPUTING QUANTUM TELEPORTATION CHAPTER 19 INTERPRETATION OF QUANTUM MECHANICS HIDDEN VARIABLES AND BELL’S INEQUALITIES THE MEASUREMENT PROBLEM SOLUTIONS TO THE MEASUREMENT PROBLEM EPILOGUE