Conten Preface Introduction 1. 1 Early Experiments 1.1.1 The Photoelectric Effect The Franck-Hertz Experiment 1.1.3 Atomic Spectroscopy 111357 Electron Diffraction Experiment 1.1.5 The Compton Effect 1.2 Early Theory 1.2.1 The Bohr Atom and the Correspondence Principle. 10 12.2 The de broglie wavelength 1.2.3 The Uncertainty Principle Wavelength revisited 12.5 he Classical radius of the electron 1.3 Units Retrospective References Problems 2 Elementary Wave Mechanics 2. 1 What is Doing the waving? 2.2 A Gedanken Experiment--Electron Diffraction Revisited The Wave Function 2.4 Finding the Wave Function-the Schrodinger Equationo 2.5 The Equation of Continuity 2.6 Separation of the Schrodinger Equation--Eigenfunctions 2.7 The General Solution to the Schrodinger Equation 8 Stationary States and Bound States Characteristics of the Eigenfunctions yn (x) 2.10 Retrospective ProblemsContents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 Introduction .................................................. 1 1.1 Early Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 The Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 The Franck–Hertz Experiment . . . . . . . . . . . . . . . . . 3 1.1.3 Atomic Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Electron Diffraction Experiments . . . . . . . . . . . . . . . 7 1.1.5 The Compton Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Early Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.1 The Bohr Atom and the Correspondence Principle . 10 1.2.2 The de Broglie Wavelength . . . . . . . . . . . . . . . . . . . . 18 1.2.3 The Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . 19 1.2.4 The Compton Wavelength Revisited . . . . . . . . . . . . 21 1.2.5 The Classical Radius of the Electron . . . . . . . . . . . . 23 1.3 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4 Retrospective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 Elementary Wave Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1 What is Doing the Waving? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 A Gedanken Experiment—Electron Diffraction Revisited . . . . . . 27 2.3 The Wave Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4 Finding the Wave Function—the Schr¨odinger Equation¨o. . . . . . . 29 2.5 The Equation of Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.6 Separation of the Schr¨odinger Equation—Eigenfunctions . . . . . . 33 2.7 The General Solution to the Schr¨odinger Equation . . . . . . . . . . . . 35 2.8 Stationary States and Bound States . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.9 Characteristics of the Eigenfunctions ψn (x) . . . . . . . . . . . . . . . . . 38 2.10 Retrospective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 xi