MOLECULAR SPECTROSCOPY

Size: px
Start display at page:

Download "MOLECULAR SPECTROSCOPY"

Transcription

1 MOLECULAR SPECTROSCOPY First Edition Jeanne L. McHale University of Idaho PRENTICE HALL, Upper Saddle River, New Jersey 07458

2 CONTENTS PREFACE xiii 1 INTRODUCTION AND REVIEW Historical Perspective Definitions, Derivations, and Discovery Review of Quantum Mechanics The Particle in a Box: A Model for Translational Energies The Rigid Rotor: A Model for Rotational Motion of Diatomics The Harmonic Oscillator: Vibrational Motion Approximate Solutions to the Schrodinger Equation Variation Method Perturbation Theory Statistical Mechanics Summary \ Problems 30 BIBLIOGRAPHY 31 2 THE NATURE OF ELECTROMAGNETIC RADIATION Introduction The Classical Description of Electromagnetic Radiation Maxwell's Equations Polarization Properties of Light Electric Dipole Radiation Propagation of Light in Matter Refraction Absorption and Emission of Light 44

3 vi Contents Effect of an Electromagnetic Field on Charged Particles Quantum Mechanical Aspects of Light Quantization of the Radiation Field Blackbody Radiation and the Planck Distribution Law The Photoelectric Effect and the Discovery of Photons Summary Problems 53 BIBLIOGRAPHY 55 3 ELECTRIC AND MAGNETIC PROPERTIES OF MOLECULES AND BULK MATTER Introduction Electric Properties of Molecules Review of Electrostatics Electric Moments Quantum Mechanical Calculation of Multipole Moments Interaction of Electric Moments with the Electric Field Polarizability and Induced Moments Frequency Dependence of Polarizability Quantum Mechanical Expression for the Polarizability Electric Properties of Bulk Matter Dielectric Permittivity Frequency Dependence of Permittivity Relationships between Macroscopic and Microscopic Properties The Local Field Problem: The Onsager and Kirkwood Models Magnetic Properties of Matter Basic Principles of Magnetism Magnetic Properties of Bulk Matter Magnetic Moments and Intrinsic Angular Momenta Summary Problems 89 BIBLIOGRAPHY 91 4 TIME-DEPENDENT PERTURBATION THEORY OF SPECTROSCOPY Introduction: Time Dependence in Quantum Mechanics Time-Dependent Perturbation Theory 94

4 Contents vii First-order Solution to the Time-Dependent Schrodinger Equation Perturbation due to Electromagnetic Radiation: Momentum versus Dipole Operator " Fermi's Golden Rule and the Time-Energy Uncertainty Principle Rate Expression for Emission Photon Density of States Fermi's Golden Rule for Stimulated and Spontaneous Emission Perturbation Theory Calculation of Polarizability Derivation of the Kramers-Heisenberg-Dirac Equation Finite State Lifetimes and Imaginary Component of Polarizability Oscillator Strength Quantum Mechanical Expression for Emission Rate Time Dependence of the Density Matrix Summary Problems 116 BIBLIOGRAPHY THE TIME-DEPENDENT APPROACH TO SPECTROSCOPY Introduction Time-Correlation Functions and Spectra as Fourier Transform Pairs Properties of Time-Correlation Functions and Spectral Lineshapes The Fluctuation-Dissipation Theorem Rotational Correlation Functions and Pure Rotational Spectra Correlation Functions for Absorption and Light Scattering Classical Free-Rotor Correlation Function and Spectrum Reorientational Spectroscopy of Liquids Dielectric Relaxation Far-Infrared Absorption Depolarized Rayleigh Scattering Vibration-Rotation Spectra Spectral Moments Summary Problems 149

5 Vlil Contents BIBLIOGRAPHY EXPERIMENTAL CONSIDERATIONS: ABSORPTION, EMIS- SION, AND SCATTERING Introduction Einstein A and B Coefficients for Absorption and Emission Absorption and Stimulated Emission Absorption and Emission Spectroscopy Atomic Spectra Molecular Electronic Spectra Measurement of Light Scattering: The Raman and Rayleigh Effects Spectral Lineshapes Summary Problems 171 BIBLIOGRAPHY ATOMIC SPECTROSCOPY Introduction Good Quantum Numbers and Not So Good Quantum Numbers The Hydrogen Atom: Energy Levels and Selection Rules Many-Electron Atoms The Clebsch-Gordan Series Spin-Orbit Coupling Selection Rules for Atomic Absorption and Emission El, Ml, and E2 Allowed Transitions Hyperfine Structure I The Effect of External Fields The Zeeman Effect The Stark Effect Atomic Lasers and the Principles of Laser Emission Summary Problems 206 BIBLIOGRAPHY ROTATIONAL SPECTROSCOPY Introduction Energy Levels of Free Rigid Rotors 209

6 Contents ix Diatomics Polyatomic Rotations Angular Momentum Coupling in Non- 1!] Electronic States Nuclear Statistics and J States of Homonuclear Diatomics Rotational Absorption and Emission Spectroscopy Rotational Raman Spectroscopy Corrections to the Rigid-Rotor Approximation Internal Rotation Free Rotation Limit, k B T» V o Harmonic Oscillator Limit, k B T «V o Summary Problems 245 BIBLIOGRAPHY VIBRATIONAL SPECTROSCOPY OF DIATOMICS Introduction The Born-Oppenheimer Approximation and Its Consequences The Harmonic Oscillator Model Selection Rules for Vibrational Transitions Infrared Spectroscopy Raman Scattering Beyond the Rigid Rotor-Harmonic Oscillator Approximation Perturbation Theory of Vibration-Rotation Energy The Morse Oscillator and Other Anharmonic Potentials Summary Problems 267 BIBLIOGRAPHY VIBRATIONAL SPECTROSCOPY OF POLYATOMIC MOLECULES Introduction Normal Modes of Vibration Classical Equations of Motion for Normal Modes Example: Normal Modes of a Linear Triatomic The Wilson F and G Matrices Group Frequencies 279

7 X Contents 10.3 Quantum Mechanics of Polyatomic Vibrations Group Theoretical Treatment of Vibrations Finding the Symmetries of Normal Modes, Symmetries of Vibrational Wavefunctions Selection Rules for Infrared and Raman Scattering Rotational Structure Anharmonicity Selection Rules at Work: Benzene Solvent Effects on Infrared Spectra Summary Problems 305 BIBLIOGRAPHY ELECTRONIC SPECTROSCOPY Introduction Diatomic Molecules: Electronic States and Selection Rules Molecular Orbitals and Electronic Configurations Term Symbols for Diatomics Selection Rules Examples of Selection Rules at Work: O 2 and I Vibrational Structure in Electronic Spectra of Diatomics Absorption Spectra Emission Spectra Dissociation and Predissociation Born-Oppenheimer Breakdown in Diatbmic Molecules Polyatomic Molecules: Electronic States and Selection Rules Molecular Orbitals and Electronic States of H 2 O Franck-Condon Progressions in Electronic Spectra of Polyatomics Benzene: Electronic Spectra and Vibronic Activity of Nontotally Symmetric Modes Transition Metal Complexes Emission Spectroscopy of Polyatomic Molecules Chromophores Solvent Effects in Electronic Spectroscopy Solvent-Induced Frequency Shifts Solvent Effects on Intensity 358

8 Contents xi Specific Solvent Effects in Electronic Spectra Summary Problems 360 BIBLIOGRAPHY RAMAN AND RESONANCE RAMAN SPECTROSCOPY Introduction Selection Rules in Raman Scattering Off-Resonance Raman Scattering Resonance Raman Scattering Polarization in Raman Scattering Polarization in Off-Resonance Raman Scattering Polarization in Resonance Raman Scattering Rotational and Vibrational Dynamics in Raman Scattering Analysis of Raman Excitation Profiles Transform Theory of Raman Intensity Time-Dependent Theory of Resonance Raman Spectra Raman Scattering as a Third-Order Nonlinear Process Summary Problems 406 BIBLIOGRAPHY 407 APPENDICES 408 A. MATH REVIEW 410 A.I Vectors and Tensors in Three Dimensions 410 A.2 Matrices 412 A.3 Operations with Cartesian and Spherical Tensors 415 A.4 Spherical Harmonics 417 A.5 Wigner Rotation Functions and Spherical Tensors 418 A.6 The Clebsch-Gordan Series and 3j Symbols 421 BIBLIOGRAPHY 423 B. PRINCIPLES OF ELECTROSTATICS 424 B.I Units 424 B.2 Some Applications of Gauss' Law 425

9 Xll Contents B.2.1 The Lorentz Model of the Atom 426 B.2.2 Electric Field within a Capacitor 426 B.3 Some Mathematical Details 427 C. GROUP THEORY 430 C.I Point Groups and Symmetry Operations 430 C.2 Information Conveyed by Character Tables 432 C.3 Direct Products and Reducible Representations 436 C.4 Character Tables 438 BIBLIOGRAPHY 448 SUBJECT INDEX 449

P. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics THIRD EDITION

P. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics THIRD EDITION P. W. Atkins and R. S. Friedman Molecular Quantum Mechanics THIRD EDITION Oxford New York Tokyo OXFORD UNIVERSITY PRESS 1997 Introduction and orientation 1 Black-body radiation 1 Heat capacities 2 The

More information

Wolfgang Demtroder. Molecular Physics. Theoretical Principles and Experimental Methods WILEY- VCH. WILEY-VCH Verlag GmbH & Co.

Wolfgang Demtroder. Molecular Physics. Theoretical Principles and Experimental Methods WILEY- VCH. WILEY-VCH Verlag GmbH & Co. Wolfgang Demtroder Molecular Physics Theoretical Principles and Experimental Methods WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA v Preface xiii 1 Introduction 1 1.1 Short Historical Overview 2 1.2 Molecular

More information

Spectra of Atoms and Molecules. Peter F. Bernath

Spectra of Atoms and Molecules. Peter F. Bernath Spectra of Atoms and Molecules Peter F. Bernath New York Oxford OXFORD UNIVERSITY PRESS 1995 Contents 1 Introduction 3 Waves, Particles, and Units 3 The Electromagnetic Spectrum 6 Interaction of Radiation

More information

Chemistry 483 Lecture Topics Fall 2009

Chemistry 483 Lecture Topics Fall 2009 Chemistry 483 Lecture Topics Fall 2009 Text PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon A. Background (M&S,Chapter 1) Blackbody Radiation Photoelectric effect DeBroglie Wavelength Atomic

More information

Fundamentals of Spectroscopy for Optical Remote Sensing. Course Outline 2009

Fundamentals of Spectroscopy for Optical Remote Sensing. Course Outline 2009 Fundamentals of Spectroscopy for Optical Remote Sensing Course Outline 2009 Part I. Fundamentals of Quantum Mechanics Chapter 1. Concepts of Quantum and Experimental Facts 1.1. Blackbody Radiation and

More information

Chemistry 881 Lecture Topics Fall 2001

Chemistry 881 Lecture Topics Fall 2001 Chemistry 881 Lecture Topics Fall 2001 Texts PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon MATHEMATICS for PHYSICAL CHEMISTRY, Mortimer i. Mathematics Review (M, Chapters 1,2,3 & 4; M&S,

More information

The Raman Effect. A Unified Treatment of the Theory of Raman Scattering by Molecules. DerekA. Long

The Raman Effect. A Unified Treatment of the Theory of Raman Scattering by Molecules. DerekA. Long The Raman Effect A Unified Treatment of the Theory of Raman Scattering by Molecules DerekA. Long Emeritus Professor ofstructural Chemistry University of Bradford Bradford, UK JOHN WILEY & SONS, LTD Vll

More information

Chem 442 Review of Spectroscopy

Chem 442 Review of Spectroscopy Chem 44 Review of Spectroscopy General spectroscopy Wavelength (nm), frequency (s -1 ), wavenumber (cm -1 ) Frequency (s -1 ): n= c l Wavenumbers (cm -1 ): n =1 l Chart of photon energies and spectroscopies

More information

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer Franz Schwabl QUANTUM MECHANICS Translated by Ronald Kates Second Revised Edition With 122Figures, 16Tables, Numerous Worked Examples, and 126 Problems ff Springer Contents 1. Historical and Experimental

More information

List of Comprehensive Exams Topics

List of Comprehensive Exams Topics List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle

More information

LECTURES ON QUANTUM MECHANICS

LECTURES ON QUANTUM MECHANICS LECTURES ON QUANTUM MECHANICS GORDON BAYM Unitsersity of Illinois A II I' Advanced Bock Progrant A Member of the Perseus Books Group CONTENTS Preface v Chapter 1 Photon Polarization 1 Transformation of

More information

CONTENTS. vii. CHAPTER 2 Operators 15

CONTENTS. vii. CHAPTER 2 Operators 15 CHAPTER 1 Why Quantum Mechanics? 1 1.1 Newtonian Mechanics and Classical Electromagnetism 1 (a) Newtonian Mechanics 1 (b) Electromagnetism 2 1.2 Black Body Radiation 3 1.3 The Heat Capacity of Solids and

More information

Modern Optical Spectroscopy

Modern Optical Spectroscopy Modern Optical Spectroscopy With Exercises and Examples from Biophysics and Biochemistry von William W Parson 1. Auflage Springer-Verlag Berlin Heidelberg 2006 Verlag C.H. Beck im Internet: www.beck.de

More information

PHYSICS. Course Syllabus. Section 1: Mathematical Physics. Subject Code: PH. Course Structure. Electromagnetic Theory

PHYSICS. Course Syllabus. Section 1: Mathematical Physics. Subject Code: PH. Course Structure. Electromagnetic Theory PHYSICS Subject Code: PH Course Structure Sections/Units Topics Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Mathematical Physics Classical Mechanics Electromagnetic

More information

ATOMIC AND LASER SPECTROSCOPY

ATOMIC AND LASER SPECTROSCOPY ALAN CORNEY ATOMIC AND LASER SPECTROSCOPY CLARENDON PRESS OXFORD 1977 Contents 1. INTRODUCTION 1.1. Planck's radiation law. 1 1.2. The photoelectric effect 4 1.3. Early atomic spectroscopy 5 1.4. The postulates

More information

Introduction to Modern Physics

Introduction to Modern Physics SECOND EDITION Introduction to Modern Physics John D. McGervey Case Western Reserve University Academic Press A Subsidiary of Harcourt Brace Jovanovich Orlando San Diego San Francisco New York London Toronto

More information

NPTEL/IITM. Molecular Spectroscopy Lectures 1 & 2. Prof.K. Mangala Sunder Page 1 of 15. Topics. Part I : Introductory concepts Topics

NPTEL/IITM. Molecular Spectroscopy Lectures 1 & 2. Prof.K. Mangala Sunder Page 1 of 15. Topics. Part I : Introductory concepts Topics Molecular Spectroscopy Lectures 1 & 2 Part I : Introductory concepts Topics Why spectroscopy? Introduction to electromagnetic radiation Interaction of radiation with matter What are spectra? Beer-Lambert

More information

Physics of atoms and molecules

Physics of atoms and molecules Physics of atoms and molecules 2nd edition B.H. Bransden and C.J. Joachain Prentice Hall An imprint of Pearson Education Harlow, England London New York Boston San Francisco Toronto Sydney Singapore Hong

More information

Quantum Mechanics: Fundamentals

Quantum Mechanics: Fundamentals Kurt Gottfried Tung-Mow Yan Quantum Mechanics: Fundamentals Second Edition With 75 Figures Springer Preface vii Fundamental Concepts 1 1.1 Complementarity and Uncertainty 1 (a) Complementarity 2 (b) The

More information

QUANTUM MECHANICS SECOND EDITION G. ARULDHAS

QUANTUM MECHANICS SECOND EDITION G. ARULDHAS QUANTUM MECHANICS SECOND EDITION G. ARULDHAS Formerly, Professor and Head of Physics and Dean, Faculty of Science University of Kerala New Delhi-110001 2009 QUANTUM MECHANICS, 2nd Ed. G. Aruldhas 2009

More information

Topics for the Qualifying Examination

Topics for the Qualifying Examination Topics for the Qualifying Examination Quantum Mechanics I and II 1. Quantum kinematics and dynamics 1.1 Postulates of Quantum Mechanics. 1.2 Configuration space vs. Hilbert space, wave function vs. state

More information

COPYRIGHTED MATERIAL. Index

COPYRIGHTED MATERIAL. Index 347 Index a AC fields 81 119 electric 81, 109 116 laser 81, 136 magnetic 112 microwave 107 109 AC field traps see Traps AC Stark effect 82, 84, 90, 96, 97 101, 104 109 Adiabatic approximation 3, 10, 32

More information

Symmetries in Quantum Physics

Symmetries in Quantum Physics Symmetries in Quantum Physics U. Fano Department of Physics and James Franck Institute University of Chicago Chicago, Illinois A. R. P. Rau Department of Physics and Astronomy louisiana State University

More information

INTRODUCTION TO MODERN VIBRATIONAL SPECTROSCOPY

INTRODUCTION TO MODERN VIBRATIONAL SPECTROSCOPY INTRODUCTION TO MODERN VIBRATIONAL SPECTROSCOPY MAX DIEM Department of Chemistry City University of New York Hunter College A Wiley-Interscience Publication JOHN WILEY & SONS New York Chichester Brisbane

More information

PRINCIPLES OF NONLINEAR OPTICAL SPECTROSCOPY

PRINCIPLES OF NONLINEAR OPTICAL SPECTROSCOPY PRINCIPLES OF NONLINEAR OPTICAL SPECTROSCOPY Shaul Mukamel University of Rochester Rochester, New York New York Oxford OXFORD UNIVERSITY PRESS 1995 Contents 1. Introduction 3 Linear versus Nonlinear Spectroscopy

More information

CHM Physical Chemistry II Chapter 12 - Supplementary Material. 1. Einstein A and B coefficients

CHM Physical Chemistry II Chapter 12 - Supplementary Material. 1. Einstein A and B coefficients CHM 3411 - Physical Chemistry II Chapter 12 - Supplementary Material 1. Einstein A and B coefficients Consider two singly degenerate states in an atom, molecule, or ion, with wavefunctions 1 (for the lower

More information

DEPARTMENT OF PHYSICS UNIVERSITY OF PUNE PUNE SYLLABUS for the M.Phil. (Physics ) Course

DEPARTMENT OF PHYSICS UNIVERSITY OF PUNE PUNE SYLLABUS for the M.Phil. (Physics ) Course DEPARTMENT OF PHYSICS UNIVERSITY OF PUNE PUNE - 411007 SYLLABUS for the M.Phil. (Physics ) Course Each Student will be required to do 3 courses, out of which two are common courses. The third course syllabus

More information

Charge and Energy Transfer Dynamits in Molecular Systems

Charge and Energy Transfer Dynamits in Molecular Systems Volkhard May, Oliver Kühn Charge and Energy Transfer Dynamits in Molecular Systems Second, Revised and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents 1 Introduction 19 2 Electronic

More information

PHYSICS-PH (PH) Courses. Physics-PH (PH) 1

PHYSICS-PH (PH) Courses. Physics-PH (PH) 1 Physics-PH (PH) 1 PHYSICS-PH (PH) Courses PH 110 Physics of Everyday Phenomena (GT-SC2) Credits: 3 (3-0-0) Fundamental concepts of physics and elementary quantitative reasoning applied to phenomena in

More information

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES)

PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 5 (TRANSITION PROBABILITIES AND TRANSITION DIPOLE MOMENT. OVERVIEW OF SELECTION RULES) Subject Chemistry Paper No and Title Module No and Title Module Tag 8 and Physical Spectroscopy 5 and Transition probabilities and transition dipole moment, Overview of selection rules CHE_P8_M5 TABLE

More information

Quantum Physics in the Nanoworld

Quantum Physics in the Nanoworld Hans Lüth Quantum Physics in the Nanoworld Schrödinger's Cat and the Dwarfs 4) Springer Contents 1 Introduction 1 1.1 General and Historical Remarks 1 1.2 Importance for Science and Technology 3 1.3 Philosophical

More information

FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES

FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES i FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES Credit units: 6 ECTS Lectures: 48 h Tapio Rantala, prof. Tue 10 12 SC203 SG219 8 10 SG312 FirstName.LastName@tut.fi http://www.tut.fi/~trantala/opetus/

More information

CHAPTER 13 Molecular Spectroscopy 2: Electronic Transitions

CHAPTER 13 Molecular Spectroscopy 2: Electronic Transitions CHAPTER 13 Molecular Spectroscopy 2: Electronic Transitions I. General Features of Electronic spectroscopy. A. Visible and ultraviolet photons excite electronic state transitions. ε photon = 120 to 1200

More information

What dictates the rate of radiative or nonradiative excited state decay?

What dictates the rate of radiative or nonradiative excited state decay? What dictates the rate of radiative or nonradiative excited state decay? Transitions are faster when there is minimum quantum mechanical reorganization of wavefunctions. This reorganization energy includes

More information

LECTURE NOTES. Ay/Ge 132 ATOMIC AND MOLECULAR PROCESSES IN ASTRONOMY AND PLANETARY SCIENCE. Geoffrey A. Blake. Fall term 2016 Caltech

LECTURE NOTES. Ay/Ge 132 ATOMIC AND MOLECULAR PROCESSES IN ASTRONOMY AND PLANETARY SCIENCE. Geoffrey A. Blake. Fall term 2016 Caltech LECTURE NOTES Ay/Ge 132 ATOMIC AND MOLECULAR PROCESSES IN ASTRONOMY AND PLANETARY SCIENCE Geoffrey A. Blake Fall term 2016 Caltech Acknowledgment Part of these notes are based on lecture notes from the

More information

Lecture Notes. Quantum Theory. Prof. Maximilian Kreuzer. Institute for Theoretical Physics Vienna University of Technology. covering the contents of

Lecture Notes. Quantum Theory. Prof. Maximilian Kreuzer. Institute for Theoretical Physics Vienna University of Technology. covering the contents of Lecture Notes Quantum Theory by Prof. Maximilian Kreuzer Institute for Theoretical Physics Vienna University of Technology covering the contents of 136.019 Quantentheorie I and 136.027 Quantentheorie II

More information

MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY

MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY MOLECULAR LIGHT SCATTERING AND OPTICAL ACTIVITY Second edition, revised and enlarged LAURENCE D. BARRON, F.R.S.E. Gardiner Professor of Chemistry, University of Glasgow 122. CAMBRIDGE UNIVERSITY PRESS

More information

Quantum. Mechanics. Y y. A Modern Development. 2nd Edition. Leslie E Ballentine. World Scientific. Simon Fraser University, Canada TAIPEI BEIJING

Quantum. Mechanics. Y y. A Modern Development. 2nd Edition. Leslie E Ballentine. World Scientific. Simon Fraser University, Canada TAIPEI BEIJING BEIJING TAIPEI Quantum Mechanics A Modern Development 2nd Edition Leslie E Ballentine Simon Fraser University, Canada Y y NEW JERSEY LONDON SINGAPORE World Scientific SHANGHAI HONG KONG CHENNAI Contents

More information

What happens when light falls on a material? Transmission Reflection Absorption Luminescence. Elastic Scattering Inelastic Scattering

What happens when light falls on a material? Transmission Reflection Absorption Luminescence. Elastic Scattering Inelastic Scattering Raman Spectroscopy What happens when light falls on a material? Transmission Reflection Absorption Luminescence Elastic Scattering Inelastic Scattering Raman, Fluorescence and IR Scattering Absorption

More information

Lectures on Quantum Mechanics

Lectures on Quantum Mechanics Lectures on Quantum Mechanics Steven Weinberg The University of Texas at Austin CAMBRIDGE UNIVERSITY PRESS Contents PREFACE page xv NOTATION xviii 1 HISTORICAL INTRODUCTION 1 1.1 Photons 1 Black-body radiation

More information

( ) x10 8 m. The energy in a mole of 400 nm photons is calculated by: ' & sec( ) ( & % ) 6.022x10 23 photons' E = h! = hc & 6.

( ) x10 8 m. The energy in a mole of 400 nm photons is calculated by: ' & sec( ) ( & % ) 6.022x10 23 photons' E = h! = hc & 6. Introduction to Spectroscopy Spectroscopic techniques are widely used to detect molecules, to measure the concentration of a species in solution, and to determine molecular structure. For proteins, most

More information

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont

MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont MODERN PHYSICS Frank J. Blatt Professor of Physics, University of Vermont McGRAW-HILL, INC. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal New Delhi

More information

DEPARTMENT OF PHYSICS

DEPARTMENT OF PHYSICS Department of Physics 1 DEPARTMENT OF PHYSICS Office in Engineering Building, Room 124 (970) 491-6206 physics.colostate.edu (http://www.physics.colostate.edu) Professor Jacob Roberts, Chair Undergraduate

More information

OPTI 511R: OPTICAL PHYSICS & LASERS

OPTI 511R: OPTICAL PHYSICS & LASERS OPTI 511R: OPTICAL PHYSICS & LASERS Instructor: R. Jason Jones Office Hours: TBD Teaching Assistant: Robert Rockmore Office Hours: Wed. (TBD) h"p://wp.op)cs.arizona.edu/op)511r/ h"p://wp.op)cs.arizona.edu/op)511r/

More information

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific

More information

V( x) = V( 0) + dv. V( x) = 1 2

V( x) = V( 0) + dv. V( x) = 1 2 Spectroscopy 1: rotational and vibrational spectra The vibrations of diatomic molecules Molecular vibrations Consider a typical potential energy curve for a diatomic molecule. In regions close to R e (at

More information

Chemistry 218 Spring Molecular Structure

Chemistry 218 Spring Molecular Structure Chemistry 218 Spring 2015-2016 Molecular Structure R. Sultan COURSE SYLLABUS Email: rsultan@aub.edu.lb Homepage: http://staff.aub.edu.lb/~rsultan/ Lectures: 12:30-13:45 T, Th. 101 Chemistry Textbook: P.

More information

Practical Quantum Mechanics

Practical Quantum Mechanics Siegfried Flügge Practical Quantum Mechanics With 78 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents Volume I I. General Concepts 1. Law of probability

More information

Students are required to pass a minimum of 15 AU of PAP courses including the following courses:

Students are required to pass a minimum of 15 AU of PAP courses including the following courses: School of Physical and Mathematical Sciences Division of Physics and Applied Physics Minor in Physics Curriculum - Minor in Physics Requirements for the Minor: Students are required to pass a minimum of

More information

510 Subject Index. Hamiltonian 33, 86, 88, 89 Hamilton operator 34, 164, 166

510 Subject Index. Hamiltonian 33, 86, 88, 89 Hamilton operator 34, 164, 166 Subject Index Ab-initio calculation 24, 122, 161. 165 Acentric factor 279, 338 Activity absolute 258, 295 coefficient 7 definition 7 Atom 23 Atomic units 93 Avogadro number 5, 92 Axilrod-Teller-forces

More information

Physical Chemistry I Fall 2016 Second Hour Exam (100 points) Name:

Physical Chemistry I Fall 2016 Second Hour Exam (100 points) Name: Physical Chemistry I Fall 2016 Second Hour Exam (100 points) Name: (20 points) 1. Quantum calculations suggest that the molecule U 2 H 2 is planar and has symmetry D 2h. D 2h E C 2 (z) C 2 (y) C 2 (x)

More information

CLASSICAL ELECTRICITY

CLASSICAL ELECTRICITY CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo

More information

CHEM6416 Theory of Molecular Spectroscopy 2013Jan Spectroscopy frequency dependence of the interaction of light with matter

CHEM6416 Theory of Molecular Spectroscopy 2013Jan Spectroscopy frequency dependence of the interaction of light with matter CHEM6416 Theory of Molecular Spectroscopy 2013Jan22 1 1. Spectroscopy frequency dependence of the interaction of light with matter 1.1. Absorption (excitation), emission, diffraction, scattering, refraction

More information

Department of Physics

Department of Physics Classical Mechanics PHY(C)-102 M. Sc. 1st Year (Sem. 1st) Newtonian mechanics of one and many particle systems; conservation laws, constraints, their classification; D' Alembert's principle, Lagrange's

More information

Quantum Physics II (8.05) Fall 2002 Outline

Quantum Physics II (8.05) Fall 2002 Outline Quantum Physics II (8.05) Fall 2002 Outline 1. General structure of quantum mechanics. 8.04 was based primarily on wave mechanics. We review that foundation with the intent to build a more formal basis

More information

Atoms and Molecules Interacting with Light Atomic Physics for the Laser Era

Atoms and Molecules Interacting with Light Atomic Physics for the Laser Era Atoms and Molecules Interacting with Light Atomic Physics for the Laser Era Peter van der Straten Universiteit Utrecht, The Netherlands and Harold Metcalf State University of New York, Stony Brook This

More information

Theoretical Photochemistry WiSe 2017/18

Theoretical Photochemistry WiSe 2017/18 Theoretical Photochemistry WiSe 2017/18 Lecture 7 Irene Burghardt (burghardt@chemie.uni-frankfurt.de) http://www.theochem.uni-frankfurt.de/teaching/ Theoretical Photochemistry 1 Topics 1. Photophysical

More information

Lecture 10 Diatomic Vibration Spectra Harmonic Model

Lecture 10 Diatomic Vibration Spectra Harmonic Model Chemistry II: Introduction to Molecular Spectroscopy Prof. Mangala Sunder Department of Chemistry and Biochemistry Indian Institute of Technology, Madras Lecture 10 Diatomic Vibration Spectra Harmonic

More information

Molecular energy levels and spectroscopy

Molecular energy levels and spectroscopy Molecular energy levels and spectroscopy 1. Translational energy levels The translational energy levels of a molecule are usually taken to be those of a particle in a three-dimensional box: n x E(n x,n

More information

Marcelo Alonso. Edward J. Finn. Georgetown University. Prentice Hall

Marcelo Alonso. Edward J. Finn. Georgetown University. Prentice Hall PHYSICS Marcelo Alonso Florida Institute of Technology Edward J. Finn Georgetown University PEARSON Prentice Hall Harlow, England " London " New York " Boston " San Francisco -Toronto Sydney " Tokyo "

More information

Lecture 7: Electronic Spectra of Diatomics

Lecture 7: Electronic Spectra of Diatomics Lecture 7: Electronic Spectra of Diatomics. Term symbols for diatomic molecules Fortrat parabola, (Symmetric Top). Common molecular models for diatomics 3. Improved treatments 4. Quantitative absorption

More information

Chapter 3. Electromagnetic Theory, Photons. and Light. Lecture 7

Chapter 3. Electromagnetic Theory, Photons. and Light. Lecture 7 Lecture 7 Chapter 3 Electromagnetic Theory, Photons. and Light Sources of light Emission of light by atoms The electromagnetic spectrum see supplementary material posted on the course website Electric

More information

Quantum Mechanics: Foundations and Applications

Quantum Mechanics: Foundations and Applications Arno Böhm Quantum Mechanics: Foundations and Applications Third Edition, Revised and Enlarged Prepared with Mark Loewe With 96 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo

More information

INTRODUCTION TO THE STRUCTURE OF MATTER

INTRODUCTION TO THE STRUCTURE OF MATTER INTRODUCTION TO THE STRUCTURE OF MATTER A Course in Modern Physics John J. Brehm and William J. Mullin University of Massachusetts Amherst, Massachusetts Fachberelch 5?@8hnlsdie Hochschule Darmstadt! HochschulstraSa

More information

M.Sc. Physics

M.Sc. Physics --------------------------------------- M.Sc. Physics Curriculum & Brief Syllabi (2012) --------------------------------------- DEPARTMENT OF PHYSICS NATIONAL INSTITUTE OF TECHNOLOGY CALICUT CURRICULUM

More information

Liquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z

Liquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z Liquid Crystals Second Edition IAM-CHOON 1(1100.,4 z 'i; BICENTCNNIAL 1 8 0 7 WILEY 2007 DICENTENNIAL n z z r WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Preface xiii Chapter 1.

More information

Molecular spectroscopy

Molecular spectroscopy Molecular spectroscopy Origin of spectral lines = absorption, emission and scattering of a photon when the energy of a molecule changes: rad( ) M M * rad( ' ) ' v' 0 0 absorption( ) emission ( ) scattering

More information

Molecular spectroscopy Multispectral imaging (FAFF 020, FYST29) fall 2017

Molecular spectroscopy Multispectral imaging (FAFF 020, FYST29) fall 2017 Molecular spectroscopy Multispectral imaging (FAFF 00, FYST9) fall 017 Lecture prepared by Joakim Bood joakim.bood@forbrf.lth.se Molecular structure Electronic structure Rotational structure Vibrational

More information

Rotation and vibration of Molecules

Rotation and vibration of Molecules Rotation and vibration of Molecules Overview of the two lectures... 2 General remarks on spectroscopy... 2 Beer-Lambert law for photoabsorption... 3 Einstein s coefficients... 4 Limits of resolution...

More information

Spectroscopy. Practical Handbook of. J. W. Robinson, Ph.D., D.Sc, F.R.C.S. Department of Chemistry Louisiana State University Baton Rouge, Louisiana

Spectroscopy. Practical Handbook of. J. W. Robinson, Ph.D., D.Sc, F.R.C.S. Department of Chemistry Louisiana State University Baton Rouge, Louisiana Practical Handbook of Spectroscopy Edited by J. W. Robinson, Ph.D., D.Sc, F.R.C.S. Department of Chemistry Louisiana State University Baton Rouge, Louisiana CRC Press Boca Raton Ann Arbor Boston TABLE

More information

NANO/MICROSCALE HEAT TRANSFER

NANO/MICROSCALE HEAT TRANSFER NANO/MICROSCALE HEAT TRANSFER Zhuomin M. Zhang Georgia Institute of Technology Atlanta, Georgia New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore

More information

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy

Spectroscopy in Inorganic Chemistry. Vibration and Rotation Spectroscopy Spectroscopy in Inorganic Chemistry Symmetry requirement for coupling combination bands and Fermi resonance 2 3 V 3 1505 cm -1 (R, IR) E' stretches v 1 888 cm -1 (R) A 1 ' stretch V 2 718 cm -1 (IR) A

More information

Module 4 : Third order nonlinear optical processes. Lecture 28 : Inelastic Scattering Processes. Objectives

Module 4 : Third order nonlinear optical processes. Lecture 28 : Inelastic Scattering Processes. Objectives Module 4 : Third order nonlinear optical processes Lecture 28 : Inelastic Scattering Processes Objectives In this lecture you will learn the following Light scattering- elastic and inelastic-processes,

More information

Lecture 0. NC State University

Lecture 0. NC State University Chemistry 736 Lecture 0 Overview NC State University Overview of Spectroscopy Electronic states and energies Transitions between states Absorption and emission Electronic spectroscopy Instrumentation Concepts

More information

Group Theory and Its Applications in Physics

Group Theory and Its Applications in Physics T. Inui Y Tanabe Y. Onodera Group Theory and Its Applications in Physics With 72 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Contents Sections marked with

More information

van Quantum tot Molecuul

van Quantum tot Molecuul 10 HC10: Molecular and vibrational spectroscopy van Quantum tot Molecuul Dr Juan Rojo VU Amsterdam and Nikhef Theory Group http://www.juanrojo.com/ j.rojo@vu.nl Molecular and Vibrational Spectroscopy Based

More information

Elementary Lectures in Statistical Mechanics

Elementary Lectures in Statistical Mechanics George DJ. Phillies Elementary Lectures in Statistical Mechanics With 51 Illustrations Springer Contents Preface References v vii I Fundamentals: Separable Classical Systems 1 Lecture 1. Introduction 3

More information

Study Plan for Ph.D in Physics (2011/2012)

Study Plan for Ph.D in Physics (2011/2012) Plan Study Plan for Ph.D in Physics (2011/2012) Offered Degree: Ph.D in Physics 1. General Rules and Conditions:- This plan conforms to the regulations of the general frame of the higher graduate studies

More information

Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and

More information

Nuclear Physics for Applications

Nuclear Physics for Applications Stanley C. Pruss'm Nuclear Physics for Applications A Model Approach BICENTENNIAL WILEY-VCH Verlag GmbH & Co. KGaA VII Table of Contents Preface XIII 1 Introduction 1 1.1 Low-Energy Nuclear Physics for

More information

eigenvalues eigenfunctions

eigenvalues eigenfunctions Born-Oppenheimer Approximation Atoms and molecules consist of heavy nuclei and light electrons. Consider (for simplicity) a diatomic molecule (e.g. HCl). Clamp/freeze the nuclei in space, a distance r

More information

Laser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford

Laser Physics OXFORD UNIVERSITY PRESS SIMON HOOKER COLIN WEBB. and. Department of Physics, University of Oxford Laser Physics SIMON HOOKER and COLIN WEBB Department of Physics, University of Oxford OXFORD UNIVERSITY PRESS Contents 1 Introduction 1.1 The laser 1.2 Electromagnetic radiation in a closed cavity 1.2.1

More information

MASTER OF SCIENCE IN PHYSICS

MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have

More information

Nanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons

Nanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons Nanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons Gang Chen Massachusetts Institute of Technology OXFORD UNIVERSITY PRESS 2005 Contents Foreword,

More information

Intro/Review of Quantum

Intro/Review of Quantum Intro/Review of Quantum QM-1 So you might be thinking I thought I could avoid Quantum Mechanics?!? Well we will focus on thermodynamics and kinetics, but we will consider this topic with reference to the

More information

PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES

PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES PHYSICS OF SEMICONDUCTORS AND THEIR HETEROSTRUCTURES Jasprit Singh University of Michigan McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico Milan Montreal

More information

Ψ t = ih Ψ t t. Time Dependent Wave Equation Quantum Mechanical Description. Hamiltonian Static/Time-dependent. Time-dependent Energy operator

Ψ t = ih Ψ t t. Time Dependent Wave Equation Quantum Mechanical Description. Hamiltonian Static/Time-dependent. Time-dependent Energy operator Time Dependent Wave Equation Quantum Mechanical Description Hamiltonian Static/Time-dependent Time-dependent Energy operator H 0 + H t Ψ t = ih Ψ t t The Hamiltonian and wavefunction are time-dependent

More information

INTRODUCTION TO ELECTRODYNAMICS

INTRODUCTION TO ELECTRODYNAMICS INTRODUCTION TO ELECTRODYNAMICS Second Edition DAVID J. GRIFFITHS Department of Physics Reed College PRENTICE HALL, Englewood Cliffs, New Jersey 07632 CONTENTS Preface xi Advertisement 1 1 Vector Analysis

More information

Math Questions for the 2011 PhD Qualifier Exam 1. Evaluate the following definite integral 3" 4 where! ( x) is the Dirac! - function. # " 4 [ ( )] dx x 2! cos x 2. Consider the differential equation dx

More information

Madhya Pradesh Bhoj (Open) University, Bhopal. Assignment Question Paper I

Madhya Pradesh Bhoj (Open) University, Bhopal. Assignment Question Paper I Subject : I- Quantum mechanics Maximum Marks : 30 Q6 Q7 Q8 Q6 Q7 Q8 Explain Direc delta function Explain Heitler -London theory of hydrogen molecule. Explain Pauli's exclusion principle. Explain orbital

More information

Spectral Resolution. Spectral resolution is a measure of the ability to separate nearby features in wavelength space.

Spectral Resolution. Spectral resolution is a measure of the ability to separate nearby features in wavelength space. Spectral Resolution Spectral resolution is a measure of the ability to separate nearby features in wavelength space. R, minimum wavelength separation of two resolved features. Delta lambda often set to

More information

Intro/Review of Quantum

Intro/Review of Quantum Intro/Review of Quantum QM-1 So you might be thinking I thought I could avoid Quantum Mechanics?!? Well we will focus on thermodynamics and kinetics, but we will consider this topic with reference to the

More information

Rotational Raman Spectroscopy

Rotational Raman Spectroscopy Rotational Raman Spectroscopy If EM radiation falls upon an atom or molecule, it may be absorbed if the energy of the radiation corresponds to the separation of two energy levels of the atoms or molecules.

More information

Rotations and vibrations of polyatomic molecules

Rotations and vibrations of polyatomic molecules Rotations and vibrations of polyatomic molecules When the potential energy surface V( R 1, R 2,..., R N ) is known we can compute the energy levels of the molecule. These levels can be an effect of: Rotation

More information

Infrared Spectroscopy

Infrared Spectroscopy Infrared Spectroscopy The Interaction of Light with Matter Electric fields apply forces to charges, according to F = qe In an electric field, a positive charge will experience a force, but a negative charge

More information

and for absorption: 2π c 3 m 2 ˆɛˆk,j a pe i k r b 2( nˆk,j +1 February 1, 2000

and for absorption: 2π c 3 m 2 ˆɛˆk,j a pe i k r b 2( nˆk,j +1 February 1, 2000 At the question period after a Dirac lecture at the University of Toronto, somebody in the audience remarked: Professor Dirac, I do not understand how you derived the formula on the top left side of the

More information

Quantum mechanics (QM) deals with systems on atomic scale level, whose behaviours cannot be described by classical mechanics.

Quantum mechanics (QM) deals with systems on atomic scale level, whose behaviours cannot be described by classical mechanics. A 10-MINUTE RATHER QUICK INTRODUCTION TO QUANTUM MECHANICS 1. What is quantum mechanics (as opposed to classical mechanics)? Quantum mechanics (QM) deals with systems on atomic scale level, whose behaviours

More information

Saturation Absorption Spectroscopy of Rubidium Atom

Saturation Absorption Spectroscopy of Rubidium Atom Saturation Absorption Spectroscopy of Rubidium Atom Jayash Panigrahi August 17, 2013 Abstract Saturated absorption spectroscopy has various application in laser cooling which have many relevant uses in

More information

Kumaun University Nainital M. Sc. Syllabi in Physics (Session Onwards) (Total Marks = 2000) Semester System Course Structure

Kumaun University Nainital M. Sc. Syllabi in Physics (Session Onwards) (Total Marks = 2000) Semester System Course Structure Kumaun University Nainital M. Sc. Syllabi in Physics (Session 2017-18 Onwards) (Total Marks = 2000) Semester System Course Structure (Total Four Semesters, 100 marks in each Paper followed by practical

More information

Chapter 6 Vibrational Spectroscopy

Chapter 6 Vibrational Spectroscopy Chapter 6 Vibrational Spectroscopy As with other applications of symmetry and group theory, these techniques reach their greatest utility when applied to the analysis of relatively small molecules in either

More information