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Spectroscopy Theory in One Dimension is an in-depth introduction to quantum chemistry using classical analytical calculus and symmetry group theory. The book employs the one-dimensional particle in a box and particle on a ring systems to develop the theoretical underpinnings of real-life spectroscopy and quantum mechanics. Wave functions, energy equations, transition intensities, and spectroscopic selection rules for absorption, emission, Rayleigh, and Raman spectra are derived and applied to explore why the sky is blue, why sunsets are red, and how quantum effects depend upon mass, size, temperature, and spectral resolution. Readers will understand how Predict three-dimensional spectroscopic behavior using one-dimensional examples Assign quantum transitions in real spectroscopic data using analytical calculus and group theory Connect the mysterious quantum mechanical wave function to everyday experiences of light and color Spectroscopy Theory in One Dimension is an ideal and accessible text for students in spectroscopy and quantum mechanics courses. Novice researchers in all physical science fields as well as experienced researchers and technicians needing an in-depth theoretical approach will find it invaluable. Cover Half Title Title Page Copyright Page Acknowledgments Foreword Preface Table of Contents Brief Contents Chapter 1: The Emergence of Quantum Mechanics 1.1 INTRODUCTION REFERENCES Chapter 2: Managing the Messy Mathematics 2.1 DATA FIRST 2.2 TRANSITION INTENSITY—THE VERTICAL AXIS IN THE SPECTRUM 2.3 TEMPERATURE DEPENDENCE 2.4 TRANSITION ENERGIES—THE HORIZONTAL AXIS IN THE SPECTRUM 2.5 THE WAVE FUNCTION 2.6 ONE-DIMENSIONAL PARTICLE IN A BOX WAVE FUNCTION REFERENCES Chapter 3: Energy and the Transition Equations 3.1 ANALYTICAL CALCULUS 3.2 INTRODUCTION 3.3 CREATING WAVE FUNCTIONS 3.4 1D PARTICLE ON A RING WAVE FUNCTIONS AND QUANTUM NUMBERS 3.5 1DPB ORTHOGONALITY 3.6 1DPB ENERGY LEVELS VIA THE SCHRÖDINGER EQUATION 3.7 1DPR ENERGIES 3.8 THE SPECTROSCOPIC TRANSITION ENERGY AND WAVELENGTH EQUATIONS 3.9 1DPR TRANSITION EQUATIONS 3.10 CONCLUSION REFERENCES Chapter 4: Into the Spectroscopic Weeds—Absorption and Emission Intensities 4.1 INTRODUCTION 4.2 ABSORPTION AND EMISSION INTENSITY OF THE 1DPB SYSTEM 4.3 ABSORPTION AND EMISSION SELECTION RULES FOR THE 1DPB SYSTEM 4.4 ABSORPTION AND EMISSION INTENSITY OF THE 1DPR SYSTEM 4.5 1DPR SELECTION RULES 4.6 CONCLUSION REFERENCE Chapter 5: Rayleigh and Raman Scattering Intensities 5.1 INTRODUCTION 5.2 SCATTERING INTENSITY OF THE 1DPB 5.3 1DPB RAMAN SCATTERING INTENSITY ANALYSIS 5.4 RAYLEIGH SCATTERING Δn = 0 5.5 1DPR SCATTERING TRANSITION MOMENT INTEGRAL 5.6 1DPR TRANSITION MOMENT INTEGRAL FOR Δn = ±2 5.7 1DPR RAYLEIGH SCATTERING TRANSITION MOMENT INTEGRAL FOR Δn = 0 5.8 CONCLUSION REFERENCES Chapter 6: The Big Picture 6.1 ABSORPTION STICK SPECTRUM FOR THE 1DPB SYSTEM 6.2 ABSORPTION STICK SPECTRUM OF THE 1DPR SYSTEM 6.3 RAMAN AND RAYLEIGH SCATTERING PHENOMENA 6.4 WAVELENGTH DEPENDENCE OF 1DPB RAYLEIGH SCATTERING 6.5 RAYLEIGH MODEL OF REFRACTIVE INDEX 6.6 WHY THE SUNSET IS RED AND THE SKY IS BLUE 6.7 STOKES AND ANTI-STOKES RAMAN SCATTERING SPECTRUM 6.8 CONCLUSION REFERENCES Chapter 7: Why Symmetry? 7.1 INTRODUCTION 7.2 EVEN AND ODD FUNCTIONS 7.3 SYMMETRY ELEMENTS 7.4 APPLICATION: 3D SYMMETRY ELEMENTS 7.5 APPLICATION: 3D SYMMETRY AND SPECTROSCOPY 7.6 SYMMETRIES OF THE DIPOLE AND POLARIZABILITY OPERATORS IN 1D 7.7 CONCLUSION REFERENCES Chapter 8: Symmetry Selection Rules for the 1D Particle in a Box 8.1 INTRODUCTION 8.2 SYMMETRY OF THE TRANSITION MOMENT INTEGRAL 8.3 ASSIGNING THE 1DPB POINT GROUP 8.4 ABSORPTION AND EMISSION SYMMETRY SELECTION RULES 8.5 SCATTERING SYMMETRY SELECTION RULES 8.6 RULE OF MUTUAL EXCLUSION 8.7 CONCLUSION REFERENCES Chapter 9: Symmetry Selection Rules for the 1D Particle on a Ring 9.1 INTRODUCTION 9.2 REVIEW OF THE 1DPR WAVE FUNCTIONS 9.3 WAVE FUNCTION SYMMETRY 9.4 ASSIGNING THE 1DPB POINT GROUP 9.5 DEGENERATE MULLIKEN NOTATIONS 9.6 SYMMETRY OF THE DIPOLE OPERATOR (LIGHT) 9.7 SCATTERING SYMMETRY SELECTION RULES 9.8 CONCLUSION REFERENCE Chapter 10: Is Symmetry Enough? What’s Missing? 10.1 INTRODUCTION 10.2 ROVIBRATIONAL SPECTROSCOPY 10.3 MOLECULAR VIBRATION 10.4 MOLECULAR ROTATION 10.5 SELECTION RULE COMPARISONS 10.6 SPECTRAL ASSIGNMENT 10.7 CONCLUSION Chapter 11: Failures of Classical Physics Revisited, and Understood 11.1 INTRODUCTION 11.2 BLACKBODY RADIATION AND THE UV CATASTROPHE 11.3 LINE SPECTRA 11.4 PHOTOELECTRIC EFFECT 11.5 HEAT CAPACITY 11.6 CONCLUSION REFERENCES Index Spectroscopy Theory in One Dimension is an in-depth introduction to quantum chemistry using classical analytical calculus and symmetry group theory. The book employs the one-dimensional particle in a box and particle on a ring systems to develop the theoretical underpinnings of real-life spectroscopy and quantum mechanics. Wave functions, energy equations, transition intensities, and spectroscopic selection rules for absorption, emission, Rayleigh, and Raman spectra are derived and applied to explore why the sky is blue, why sunsets are red, and how quantum effects depend upon mass, size, temperature, and spectral resolution. Readers will understand to: Predict three-dimensional spectroscopic behavior using one-dimensional examples; Assign quantum transitions in real spectroscopic data using analytical calculus and group theory; Connect the mysterious quantum mechanical wave function to everyday experiences of light and color