Overview of Topics in "Computational Chemistry 1"

1. Basic UNIX and Chemistry Software
   1. UNIX software
      1. getting started with LINUX
      2. basic UNIX commands
      3. vi
      4. ghostview - viewing postscript files
      5. pbs - a queueing system
   2. application software I
      1. Gaussian
         1. input files for Gaussian 03
         2. running Gaussian jobs through a queueing system
         3. output files generated by Gaussian 03
      2. GaussView
      3. Molden
2. geometry optimization - what is the preferred structure of molecules?
   1. geometry definition in Gaussian 03
   2. coordinate systems
      1. using symmetry
      2. internal coordinates
      3. cartesian coordinates
      4. redundant internal coordinates
      5. geometry optimization - basic considerations
      6. Newton-Raphson (NR) optimization
      7. comparative examples
   3. transition state optimization
      1. scanning bond distances, bond angles, and dihedral angles
      2. eigenvector following with the Berny algorithm
      3. global search algorithms: STQN
   4. reaction path following
      1. following the reaction pathway - choosing direction, stepsize, and convergence parameters
      2. a worked example
      3. choosing a coordinate system
3. Searching conformational space with Force Field methods
   1. force field methods
   2. force field calculations in Gaussian 03
   3. force field calculation with TINKER
4. 2nd derivatives - calculating molecular vibrations
   1. vibrational frequencies - practical considerations
   2. assigning vibrational frequencies
   3. the effects of isotopic substitution
5. thermochemistry I - connecting experiment and theory
   1. basic considerations
   2. reaction energetics
   3. Arrhenius and Eyring equations
6. theoretical methods - where does the energy come from?
   1. Hartree-Fock (HF) theory
      1. basic considerations
      2. treating open shell systems: RHF, UHF, ROHF
      3. convergence of SCF calculations
      4. stability of wavefunctions
      5. performance considerations
   2. density functional theory (DFT)
   3. semiempirical methods
   4. Application software II: MOPAC
   5. correlated methods
7. basis sets for molecular system
   1. minimal basis sets (STO-xG)
   2. split valence basis sets
   3. polarization functions (p,d,f,g)
   4. diffuse basis functions
   5. extended basis sets
   6. correlation consistent basis sets
   7. the basis set superposition error (BSSE)
8. inspecting molecular orbitals
   1. from the Gaussian output file
   2. with MOLDEN
   3. with GaussView
9. population analysis - where really are these electrons?
   1. the Mulliken population analysis
   2. the Natural Bond Orbital (NBO) Analysis
   3. inspecting the molecular electrostatic potential
   4. fitting the molecular electrostatic potential I: CHELPG
   5. fitting the molecular electrostatic potential II: Merz-Singh-Kollman (MK)
   6. the Atoms in Molecules analysis (AIM)
   7. calculating the (Pauling bond order )

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last changes: 24.04.2009, HZ
questions & comments to: zipse@cup.uni-muenchen.de

CHEM 658, ADVANCED PHYSICAL CHEMISTRY

COURSE OBJECTIVES

Quantum chemistry uses high-level mathematics as a tool to understand atomic and molecular structure and properties, as well as chemical reactivity. The purpose of this course is to provide an introduction to the mathematical foundations of quantum chemistry, as well as a practical, hands-on experience with a quantum mechanics software package.

We will derive the Schrödinger Eq. for one quantum mechanical particle (electron) in one dimension. Over the next few weeks, we will learn how to solve the Schrödinger Eq. rigorously for model systems and for atoms. There will not be sufficient time to give a detailed description of the quantum mechanical treatment of molecules. However, the laboratory sessions will immediately start with techniques for calculating molecular structure and properties. There are many software programs available which one can use as a "black box" to carry out various types of quantum mechanical calculations without being an expert in the field. We will use the Spartan program from Wavefunction, Inc. The program allows graphical input of molecular structure, menu-driven input to quantum chemistry calculational programs, and graphical analysis of molecular properties. However, the difficulty lies in knowing what type of quantum mechanical model (or approximation) is appropriate for the system under study and in interpreting the results. For that reason, we will survey the semi-empirical, ab initio, and molecular mechanics techniques used by the software package to calculate molecular structure and properties. The recommended Additional Readings should help clarify the strengths and weaknesses of each of these techniques. Each student will formulate and carry out a short research project using Spartan. An important part of this exercise will be in choosing a molecular orbital technique appropriate to the project.

Syllabus

Lecture Notes

Additional Notes

Additional Readings

Problem Set Assignments

Problem Set Answers

How to Prepare the Project

Spartan

QUANTUM CHEMISTRY

WHY STUDY QUANTUM CHEMISTRY?


MODEL SYSTEM: PARTICLE IN A BOX

MATHEMATICAL & PHYSICAL CONCEPTS IN QUANTUM MECHANICS

THE HARMONIC OSCILLATOR

ANGULAR MOMENTUM

Homepage of Walter Johnson (Notre Dame University)

Walter R. Johnson
Frank M. Freimann Professor of Physics (Emeritus)
Department of Physics
225 Nieuwland Science
University of Notre Dame
Notre Dame, IN 46556
Tel. (574) 631-1164
Fax. (574) 631-5952
Cell. (574) 274-7048
email: johnson@nd.edu

Teaching Material

Course Material for Physics 356 E&M -- Fall (2003) (WebCT)

Course Material for Physics 357 Electromagnetic Waves -- Spring (2004) (WebCT)

Course Material for Physics 80301 Atomic Physics I -- Fall (2005)

Material for C. E. A. Lectures -- July (2005)

Course Material for Physics 70006 E&M I -- Spring (2006)

Meeting with Physics Grad. Students (circa 1965).

https://www3.nd.edu/~johnson/

Atomic & Molecular Physics

Module – 1 " History of Atomic & Molecular Physics and basic backgrounds"

Lecture – 1: Introduction to Atomic and Molecular Physics

Lecture – 2: A brief history of the development of structure of atom

Lecture – 3: Formulation of Old Quantum theory

Lecture – 4: Quantization of radiation and matter: Wave-Particle duality

Lecture – 5: Electromagnetic Radiation – Matter Interactions

Lecture – 6: Radiative transitions and spectral broadening


Module – 2 "Atomic physics and atomic structure"

Lecture 7 Quantum Mechanical treatment of One-electron atoms

Lecture 8 : Quantum Mechanical treatment of One-electron atoms : radial part

Lecture 9 : Interpretation of wavefunction and modification forAlkali atoms

Lecture 10 : ALKALI SPECTRA

Lecture 11 Helium Atom

Lecture 12 : Central Field Approximation 

Lecture 13 : Title : Coupling of angular momentum

Lecture 14: Evaluation of Terms of an atom

Lecture 15 : Evaluation of coupled wavefunction  

Lecture 16 : Wigner-Eckart theorem

Lecture 17 :Fine structure : Spin-orbit coupling

Lecture 18 : Fine Structure : multi-electron atoms

Lecture 19 : j-j coupling

Lecture 20: Effect of Static Magnetic field on the spectral lines

Lecture 21: Hyperfine Structure of Spectral Lines

Lecture 22 Zeeman effect in Hyperfine structures

Lecture 23 : Electron Spin resonance spectroscopy

Lecture 24 : Nuclear magnetic resonance spectroscopy (N.M.R)

Lecture 25 : X- Ray Spectra

Module – 3 "Molecular physics and molecular structure"

Lecture 26 : Fundamentals of the Quantum Theory of molecule formation 

Lecture 27 : Understanding of Molecular Orbital  

Lecture 28 : Diatomic Molecule : Vibrational and Rotational spectra

Lecture 29: The rotational-vibrational spectra

Lecture 30 : Raman Scattering   

Lecture 31 : Vibrational structure of electronic transition

Lecture 32 : Rotational structure of particular electronic transition

Lecture 33 : Intensity distribution in the electronic vibrational structure

Lecture 34 : Term values of the electronic states of the molecule

PHYS261: Atomic Physics and Physical Optics

2016_08_25 Introduction part 1            Quantum Mechanics, Hydrogen atom, Spectra, Laplace operator            Links to older files 2016_08_31 Introduction part 2            Hydrogen atom, Spectra, wavefunctions, visualization 2016_09_01 Helium start with Introduction part 3            Hydrogen atom, Spectra, wavefunctions, visualization            Helium atom - The model; Parahelium, orthohelium; Pauli principle 2016_09_07 Helium part 2            Helium atom - Parahelium, orthohelium; Pauli principle            Electron Spin; Two spins; Singlets and Triplets; Started Approximations 2016_09_08 Helium part 3            Mainly ground state - two 1s electrons: APPROXIMATIONS            Independent hydrogen-like; repulsion included; Variational Method 2016_09_14 Helium part 4            Correlations - Hylleraas variational method, Exchange interaction            Doubly excited states 2016_09_15 Many Electron Atoms part 1            Many electron atoms - experimental facts and "Laws"            Periodic systems - failure of the hydrogen-like filled shells            Interaction with a charged cloud - SELFCONSISTENT FIELD 2016_09_21 Many Electron Atoms part 2                 Many electron atoms - expectation value of energy            Many electron atoms - variational 2016_09_22 Many Electron Atoms part 3                 Many electron atoms - variational - more details            Meaning of the notation - connection with Hartree method            Nonlocal nature of the exchange potential 2016_09_28 and 2016_09_29 External Lecture and Colloquium            DFT and work with Two-electron atoms 2016_10_06 Physical Optics 1.                 Introduction - Maxwell's Equations 2016_10_12 Physical Optics 2.                 More on Maxwell's Equations, so called Gaussian units 2016_10_13 Physical Optics 3.                 Reflection and refraction - boundary conditions - part 1 2016_10_19 Physical Optics 4.                 Reflection and refraction -part 2 - Polarization - Brewster 2016_10_20 Physical Optics 5.                 Diffraction - Circular and rectangular Aperture 2016_10_26 Light and Atoms Part 1            Time Developement in Quantum Mechanics 2016_10_27 Light and Atoms Part 2            Time Developement - Fermi Golden Rule - Transitions            Exponential Decay - Natural Line Width            SO CALLED Time - Energy Uncertainety            Density of states - in Fermi Golden Rule 2016_11_02 Light and Atoms Part 3            Continuous systems --> Coupled Vibrations --> Normal modes / Eigenmodes            Algebraic Method for an Harmonic Oscillator - Creation and Anihilation 2016_11_03 Light and Atoms Part 4            The atom + field system; The interaction            Applying the golden Rule            Approximations - The dipole Approximation etc 2016_11_09 Light and Atoms Part 5            Sponntaneous Emission rate - details            Stimulated emission - and simple introduction to lasers 2016_11_10 Additional Topics and Discussions            e.g. Diagonalization of Hamiltonians - and Golden Rule            Modifying presentations

Quantum Mechanics I and Quantum Mechanics II

Quantum Mechanics I

Quantum Mechanics II

Physical Chemistry II

• Contents
• Lecture #  : Fundamentals
  • i Classical Mechanics - Review
  • ii Quantum Mechanics vs. Classical Mechanics
  • iii Wave-Particle Duality
• Lecture #  : Configuration Spaces
  • iv Wave Functions
• Lecture #  : The Schrödinger Equation
  • Schrödinger Equations
• Lecture #  : Observables
  • vi Operators
  • vii Uncertainty Principle
• Lecture #  : Solvable Models I
  • viii Molecular Motion - Translations, Rotations, Vibrations
  • ix Particle in a Box
• Lecture #  : Solvable Models II
  • x Tunneling
  • xi Vibrations - The Harmonic Oscillator
• Lecture #  : Solvable Models III
  • xii Rotations about the Center of Mass
  • xiii Spin
  • xiv Perturbation Theory and the Variational Principle
• Lecture #  : Single-Electron Atoms
  • xv Rydberg Atoms
• Lecture #  : Many Electron Atoms I
  • xvi Many-Electron Atoms I
  • xvii Spectra
• Lecture #  : Many-Electron Atoms II
  • xviii Spectral Term Symbols
  • xix Term Symbols of Nitrogen
• Lecture #  : The Story So Far
  • xx Summary: Quantum Mechanics and General Methods
• Lecture #  : Molecules I
  • xxi The Molecular Hamiltonian
• Lecture #  : The  Molecule
  • xxii Valence Bond Theory of  Molecule
  • xxiii Molecular Orbital Theory for 
  • xxiv VB vs MO Theory for 
• Lecture #  : Molecules II
  • xxv Valence Bond Theory - General
  • xxvi Molecular Orbital Theory - General
  • Hückel Theory
• Lecture #  : Spectroscopy I
  • xxviii Introduction to Spectroscopy
• Lecture #  : Spectroscopy II
  • xxix Classical Spectroscopy
  • xxx Rotational Spectra
• Lecture #  : Spectroscopy III
  • xxxi Vibrational Spectra of Diatomics
  • xxxii Anharmonicity
• Lecture #  : Spectroscopy IV
  • xxxiii Vibrational Spectra of Polyatomics
  • xxxiv Electronic Transitions
• Lecture #  : Spectroscopy V
  • xxxv LASERs
• Appendix #  : Symmetry I
  • A Why Symmetry is Important
• Appendix #  : Symmetry II
  • B Symmetry Operations and Elements
  • C Classifying Molecules
  • D Hamiltonian and Symmetries
• Appendix #  : Symmetry III
  • E Matrix Representations
  • F Character Tables
  • G Orbital Overlap and Selection Rules

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Next: Contents Up: CHEM 3412

edu@theor.chemistry.gatech.edu
1998 © R.Hernandez

A Brief Review of Elementary Quantum Chemistry

C. David Sherrill
School of Chemistry and Biochemistry
Georgia Institute of Technology

Last Revised on 27 January 2001

• Contents
• The Motivation for Quantum Mechanics
  • The Ultraviolet Catastrophe
  • The Photoelectric Effect
  • Quantization of Electronic Angular Momentum
  • Wave-Particle Duality
• The Schrödinger Equation
  • The Time-Independent Schrödinger Equation
  • The Time-Dependent Schrödinger Equation
• Mathematical Background
  • Operators
    • Operators and Quantum Mechanics
    • Basic Properties of Operators
    • Linear Operators
    • Eigenfunctions and Eigenvalues
    • Hermitian Operators
    • Unitary Operators
  • Commutators in Quantum Mechanics
  • Linear Vector Spaces in Quantum Mechanics
• Postulates of Quantum Mechanics
• Some Analytically Soluble Problems
  • The Particle in a Box
  • The Harmonic Oscillator
  • The Rigid Rotor
  • The Hydrogen Atom
• Approximate Methods
  • Perturbation Theory
  • The Variational Method
• Molecular Quantum Mechanics
  • The Molecular Hamiltonian
  • The Born-Oppenheimer Approximation
  • Separation of the Nuclear Hamiltonian
• Solving the Electronic Eigenvalue Problem
  • The Nature of Many-Electron Wavefunctions
  • Matrix Mechanics
• Bibliography
• About this document ...

---

David Sherrill 2006-08-15

Quantum Physics

(UCSD Physics 130)

April 2, 2003

Course Summary

• Problems with Classical Physics
• Thought Experiments on Diffraction
• Probability Amplitudes
• Wave Packets and Uncertainty
• Operators
• Expectation Values
• Commutators
• The Schrödinger Equation
• Eigenfunctions, Eigenvalues and Vector Spaces
• A Particle in a Box
• Piecewise Constant Potentials in One Dimension
• The Harmonic Oscillator in One Dimension
• Delta Function Potentials in One Dimension
• Harmonic Oscillator Solution with Operators
• More Fun with Operators
• Two Particles in 3 Dimensions
• Identical Particles
• Some 3D Problems Separable in Cartesian Coordinates
• Angular Momentum
• Solutions to the Radial Equation for Constant Potentials
• Hydrogen
• Solution of the 3D HO Problem in Spherical Coordinates
• Matrix Representation of Operators and States
• A Study of  Operators and Eigenfunctions
• Spin 1/2 and other 2 State Systems
• Quantum Mechanics in an Electromagnetic Field
• Local Phase Symmetry in Quantum Mechanics and the Gauge Symmetry
• Addition of Angular Momentum
• Time Independent Perturbation Theory
• The Fine Structure of Hydrogen
• Hyperfine Structure
• The Helium Atom
• Atomic Physics
• Molecules
• Time Dependent Perturbation Theory
• Radiation in Atoms
• Classical Field Theory
• The Classical Electromagnetic Field
• Quantization of the EM Field
• Scattering of Photons
• Electron Self Energy
• The Dirac Equation
• The Dirac Equation

---

Jim Branson 2013-04-22

Physical Chemistry: Quantum Chemistry andMolecular Interactions

Table of Contents

---

• Cover

  1

• Table of Contents

  3

• Chapter A

  7

• Chapter 4

  41

Courses in Quantum Mechanics

• Introduction
  • Intended audience
  • Major Sources
  • Aim of Course
  • Outline of Course
• Probability Theory
  • Introduction
  • What is Probability?
  • Combining Probabilities
  • Mean, Variance, and Standard Deviation
  • Continuous Probability Distributions
    • Exercises
• Wave-Particle Duality
  • Introduction
  • Wavefunctions
  • Plane Waves
  • Representation of Waves via Complex Functions
  • Classical Light Waves
  • Photoelectric Effect
  • Quantum Theory of Light
  • Classical Interference of Light Waves
  • Quantum Interference of Light
  • Classical Particles
  • Quantum Particles
  • Wave Packets
  • Evolution of Wave Packets
  • Heisenberg's Uncertainty Principle
  • Schrödinger's Equation
  • Collapse of the Wave Function
    • Exercises
• Fundamentals of Quantum Mechanics
  • Introduction
  • Schrödinger's Equation
  • Normalization of the Wavefunction
  • Expectation Values and Variances
  • Ehrenfest's Theorem
  • Operators
  • Momentum Representation
  • Heisenberg's Uncertainty Principle
  • Eigenstates and Eigenvalues
  • Measurement
  • Continuous Eigenvalues
  • Stationary States
    • Exercises
• One-Dimensional Potentials
  • Introduction
  • Infinite Potential Well
  • Square Potential Barrier
  • WKB Approximation
  • Cold Emission
  • Alpha Decay
  • Square Potential Well
  • Simple Harmonic Oscillator
    • Exercises
• Multi-Particle Systems
  • Introduction
  • Fundamental Concepts
  • Non-Interacting Particles
  • Two-Particle Systems
  • Identical Particles
    • Exercises (N.B. Neglect spin in the following questions.)
• Three-Dimensional Quantum Mechanics
  • Introduction
  • Fundamental Concepts
  • Particle in a Box
  • Degenerate Electron Gases
  • White-Dwarf Stars
    • Exercises
• Orbital Angular Momentum
  • Introduction
  • Angular Momentum Operators
  • Representation of Angular Momentum
  • Eigenstates of Angular Momentum
  • Eigenvalues of 
  • Eigenvalues of 
  • Spherical Harmonics
    • Exercises
• Central Potentials
  • Introduction
  • Derivation of Radial Equation
  • Infinite Spherical Potential Well
  • Hydrogen Atom
  • Rydberg Formula
    • Exercises
• Spin Angular Momentum
  • Introduction
  • Spin Operators
  • Spin Space
  • Eigenstates of  and 
  • Pauli Representation
  • Spin Precession
    • Exercises
• Addition of Angular Momentum
  • Introduction
  • General Principles
  • Angular Momentum in the Hydrogen Atom
  • Two Spin One-Half Particles
    • Exercises
• Time-Independent Perturbation Theory
  • Introduction
  • Improved Notation
  • Two-State System
  • Non-Degenerate Perturbation Theory
  • Quadratic Stark Effect
  • Degenerate Perturbation Theory
  • Linear Stark Effect
  • Fine Structure of Hydrogen
  • Zeeman Effect
  • Hyperfine Structure
• Time-Dependent Perturbation Theory
  • Introduction
  • Preliminary Analysis
  • Two-State System
  • Spin Magnetic Resonance
  • Perturbation Expansion
  • Harmonic Perturbations
  • Electromagnetic Radiation
  • Electric Dipole Approximation
  • Spontaneous Emission
  • Radiation from a Harmonic Oscillator
  • Selection Rules
  •  Transitions in Hydrogen
  • Intensity Rules
  • Forbidden Transitions
• Variational Methods
  • Introduction
  • Variational Principle
  • Helium Atom
  • Hydrogen Molecule Ion
• Scattering Theory
  • Introduction
  • Fundamentals
  • Born Approximation
  • Partial Waves
  • Determination of Phase-Shifts
  • Hard Sphere Scattering
  • Low Energy Scattering
  • Resonances
• About this document ...

---

Richard Fitzpatrick 2010-07-20

Graduate Quantum Mechanics Lectures

Michael Fowler, UVa.

These notes cover the essential core topics of a standard graduate quantum mechanics course. The main text used for the class was Shankar, with Sakurai as a secondary text. I also adapted material from Landau, Baym and Messiah. The first lectures here review undergraduate quantum and modern physics as a reminder, this optional material was only covered briefly in class. Towards the end of the course, I added lectures on the Dirac equation, the Berry phase and graphene, not included here. I may upload them later.

http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/

Teaching Physics ( Dr. Abdalla Obeidat)

Undergraduate Course

• Phys101
• Phys101A
• Phys102
• Phys102A
• Phys103
• Phys200
• Phys201
• Phys301
• Phys303
• Phys312
• Phys351
• Phys352
• Phys461
• Phys493

Graduate Courses

• Phys701
• Phys704
• Phys711
• Phys751
• Phys752
• Phys761
• Phys791
• Phys795
• Phys798

http://www.just.edu.jo/~aobeidat/

Atomic Physics

P. Ewart

Contents 

1 Introduction 1
2 Radiation and Atoms 1
3 The Central Field Approximation 9
4 Corrections to the Central Field: Spin-Orbit interaction 17
5 Two-electron Atoms: Residual Electrostatic Effects and LS-Coupling 30
6 Nuclear Effects on Atomic Structure 37
7 Selection Rules 42
8 Atoms in Magnetic Fields 44
9 X-Rays: transitions involving inner shell electrons 56
10 High Resolution Laser Spectroscopy 61

https://users.physics.ox.ac.uk/~ewart/Atomic%20Physics%20lecture%20notes%20C%20port.pdf

Quantum Mechanics

Richard Fitzpatrick

Professor of Physics


The University of Texas at Austin

• • Major Sources
  • Purpose of Course
• Fundamental Concepts
  • Breakdown of Classical Physics
  • Photon Polarization
  • Fundamental Principles of Quantum Mechanics
  • Ket Space
  • Bra Space
  • Operators
  • Outer Product
  • Eigenvalues and Eigenvectors
  • Observables
  • Measurements
  • Expectation Values
  • Degeneracy
  • Compatible Observables
  • Uncertainty Relation
  • Continuous Spectra
  • Exercises
• Position and Momentum
  • Introduction
  • Poisson Brackets
  • Wavefunctions
  • Schrödinger Representation
  • Generalized Schrödinger Representation
  • Momentum Representation
  • Uncertainty Relation
  • Displacement Operators
  • Exercises
• Quantum Dynamics
  • Schrödinger Equation of Motion
  • Heisenberg Equation of Motion
  • Ehrenfest Theorem
  • Schrödinger Wave Equation
  • Exercises
• Orbital Angular Momentum
  • Orbital Angular Momentum
  • Eigenvalues of Orbital Angular Momentum
  • Rotation Operators
  • Eigenfunctions of Orbital Angular Momentum
  • Motion in Central Field
  • Energy Levels of Hydrogen Atom
  • Exercises
• Spin Angular Momentum
  • Introduction
  • Properties of Spin Angular Momentum
  • Wavefunction of Spin One-Half Particle
  • Rotation Operators in Spin Space
  • Magnetic Moments
  • Spin Precession
  • Pauli Two-Component Formalism
  • Spin Greater Than One-Half Systems
  • Exercises
• Addition of Angular Momentum
  • Introduction
  • Analysis
  • Exercises
• Time-Independent Perturbation Theory
  • Introduction
  • Two-State System
  • Non-Degenerate Perturbation Theory
  • Quadratic Stark Effect
  • Degenerate Perturbation Theory
  • Linear Stark Effect
  • Fine Structure
  • Zeeman Effect
  • Hyperfine Structure
  • Exercises
• Time-Dependent Perturbation Theory
  • Introduction
  • General Analysis
  • Two-State System
  • Spin Magnetic Resonance
  • Dyson Series
  • Sudden Perturbations
  • Energy-Shifts and Decay-Widths
  • Harmonic Perturbations
  • Absorption and Stimulated Emission of Radiation
  • Electric Dipole Approximation
  • Spontaneous Emission
  • Exercises
• Scattering Theory
  • Introduction
  • Fundamental Equations
  • Born Approximation
  • Partial Waves
  • Optical Theorem
  • Determination of Phase-Shifts
  • Hard Sphere Scattering
  • Low Energy Scattering
  • Resonance Scattering
  • Exercises
• Identical Particles
  • Permutation Symmetry
  • Symmetrization Postulate
  • Two-Electron System
  • Helium Atom
  • Exercises
• Relativistic Electron Theory
  • Introduction
  • Dirac Equation
  • Lorentz Invariance of Dirac Equation
  • Free Electron Motion
  • Electron Spin
  • Motion in Central Field
  • Fine Structure of Hydrogen Energy Levels
  • Positron Theory
  • Exercises
• About this document ...