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HarvardX: Chem160 The Quantum World

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Introduction to the Course
Welcome to The Quantum World
Introduction
Course Organization
Staff Introductions
Policies
Extra Resources
How to do edX Homework
Doing edX Homework
Basic Questions
Complex Questions
Final Notes
Syllabus Quiz
Syllabus Quiz, Part 1
Syllabus Quiz, Part 2
How to do Python
How to do Python
First Python Exercise
Entrance Survey
Pre-Course Survey
Pencasts: Mathematics Review
Review of Vector Analysis
Vector Calculus
Coordinate Systems
Complex Numbers
Dirac's Delta Function
Exercises: Mathematics Review
Vector Analysis
Vector Calculus
Coordinate Systems
Classical Mechanics
Classical Mechanics
Length Scales and Time Scales
Classical Motion: Newton’s Apple
Classical Motion: Analytical vs Numerical Methods
The Hamiltonian Method and Phase Space
Molecular Mechanics
Pencasts
Newton's Second Law
Work and Energy
Hamilton's Equations
Orbital Motion
Phase Space
Exercises
Newtonian Mechanics
Hamiltonian Mechanics
Orbital Motion
Extra Credit
Newtonian Mechanics
Hamiltonian Mechanics
Orbital Motion
Python
Python
Optional Feedback
Quick Survey
Waves and Quantum Mechanics
Waves and Quantum Mechanics I
Waves and Interference
The Wave Equation
Self-Adjoint Operators
Waves and Quantum Mechanics II
Eigenfunctions and Eigenvalues
Arbitrary Waves
Recap
Pencasts
The Wave Equation
Boundary Conditions
Eigenfunctions of Differential Equations
Exercises
The Wave Equation
Boundary Conditions
Eigenfunctions of Differential Operators
Extra Credit
The Wave Equation
Eigenfunctions of Differential Operators
Python
Python
Optional Feedback
Quick Survey
Postulates of Quantum Mechanics I
Classical Background
Phase Space
Classical Probability Distributions
Expectation Values
Quantum Theory First Steps
Postulate 1: The Wavefunction
Quantum Particle in a Box
Falstad
Postulate 4: Expectation Values
Wrap-up
Pencasts
Overview of the Postulates
Postulate 1 - The Wave Function
Postulate 2 - Observables
Exercises
Postulate 1 - The Wavefunction
Postulates 2 and 3 - Observables and Measurements
Extra Credit
Postulate 1 - The Wavefunction
Postulates 2 and 3 - Observables and Measurements
No Python
No Python in This Chapter
Optional Feedback
Quick Survey
Postulates of Quantum Mechanics II
Observables
Postulate 2: Observables
Eigenfunctions and eigenvalues
Hamiltonian for a Particle in a Box
Connection to the Loaded String
Falstad
Measurement
Postulate 3: Measurement
Falstad
Probability of Measuring a Particular Eigenvalue
Schrödinger’s Cat
Expectation Values
Pencasts
Postulate 3 - Measurements
Postulate 4 - Expectation Values
Postulate 5 - Time-Dependent Schrödinger Equation
Exercises
Postulate 4 - Expectation Values
Postulate 5 - Time-dependent Schrödinger Equation
Extra Credit
Postulate 5 - Time-dependent Schrödinger Equation
Python
Python
Optional Feedback
Quick Survey
The Schrödinger Equation
The Schrödinger Equation
Classical vs Quantum Mechanics
The Schrödinger Equation
Phasors
Falstad, Part 1
Falstad, Part 2
Falstad, Part 3
The Quantum Simple Harmonic Oscillator (SHO)
Chemical Bonding
Quantum Simple Harmonic Oscillator
Hermite Polynomials
Simple Harmonic Oscillator Eigenfunctions
Falstad: SHO Eigenfunctions
Pencasts
The Time-Independent Schrödinger Equation
The Harmonic Oscillator
The Harmonic Oscillator (corrections)
Properties of Matrices
Exercises
The Harmonic Oscillator
Extra Credit
The Harmonic Oscillator
No Python
No Python in This Chapter
Optional Feedback
Quick Survey
The Finite Difference Method
A Discrete Domain
Intro to the Finite Difference Method
FDM for The Schrödinger Equation
FDM and Matrices
Matrix Representation of Operators
The Matrix Eigenvalue Problem
Solving Quantum Mechanics Problems Numerically
Solving Eigenvalue Problems
Discrete Particle in a Box
Arbitrary Potentials
Falstad, Double Well
Poor Man's Molecule in a Box
Wrap-up
Pencasts
The Finite Differences Method
Poor Man's Molecule Simplified
Poor Man's Molecule Simplified (continued)
Exercises
The Method of Finite Differences
Python
Python
Optional Feedback
Quick Survey
Multidimensional Quantum Mechanics
The Multidimensional SHO
Introduction
Solving the 2D SHO
Falstad
Molecular Vibrations
Molecular Vibrations, Classical
Physical Interpretation
Extending to the General Molecule
Quantizing the 2D SHO
Solving the Quantum 2D SHO
Pencasts
2-D Isotropic Harmonic Oscillator
Classical Normal Modes of a Linear Triatomic
Quantum Normal Modes of a Linear Triatomic
Quantum Normal Modes (General Theory)
Exercises
Normal Modes
2-D Isotropic Harmonic Oscillator
Python
Python
Optional Feedback
Quick Survey
Infrared Spectroscopy
Spectroscopy Basics
Molecular Spectroscopy
Non-Linear Spectroscopy
Molecular Charge Densities
Spectroscopy Realities
Time-Dependent Fields
The Quantum SHO Model
Resonance
Transition Probabilities
How the Wave Function Changes in Time
Transition Probabilities
Frequency Response
Wrap-up
Pencasts
The Multipole Expansion
Approximate Solution to the Time-Dependent Schrödinger Equation
The Infrared Absorption Spectrum
Exercises
The Infrared Absorption Spectrum
Extra Credit
The Infrared Absorption Spectrum
Python
Python
Optional Feedback
Quick Survey
Quantum Mechanics in Momentum Space
Living in Momentum Space
The Momentum Operator
Momentum Representation Properties
Schrödinger Equation in Momentum Space
Classical and Quantum Soccer Ball
The Momentum Space Eigenfunctions
Falstad
Momentum Space Examples
Quantum SHO and The Heisenberg Uncertainty Principle
The HUP and Phase Space
Falstad
Inverse Eckardt Well
Wrap-up
Pencasts
Properties of the Momentum Eigenfunctions
The Momentum-Space Schrödinger Equation
The Particle in a Box in Momentum Space
The Harmonic Oscillator in Momentum Space
Heisenberg's Uncertainty Principle
Exercises
The Momentum-Space Schrödinger Equation
Extra Credit
The Momentum Space Schrödinger Equation
Python
No Python in This Chapter
Optional Feedback
Quick Survey
Quantum Phase Space
Classical Phase Space
Classical Phase Space
The Boltzmann Distribution
The Equipartition Theorem
Quantum Phase Space
The Wigner DIstribution
The Wigner Distribution for a Particle in a Box
Wigner Distribution for the Harmonic Oscillator States
Wigner Distribution Equation of Motion
Example: Absorption of Light
Classical vs Quantum Distributions, SHO
Wrap-up
Pencasts
Properties of Classical Phase Space
Liouville's Theorem
The Wigner "Quasi-Probability" Distribution
The Wigner "Quasi-Probability" Distribution (continued)
Wigner Distribution for the Harmonic Oscillator
Wigner Distribution of a Gaussian Wavepacket in a Harmonic Potential
Schrödinger's Equation in Phase Space
Exercises
The Wigner Quasi-Probability Distribution
Extra Credit
The Wigner Quasi-Probability Distribution
Python
Python
Optional Feedback
Quick Survey
Chemical Reactions
Quantum Mechanics and Chemical Reactions
What is a Chemical Reaction?
Example: SN2 Reaction
Classical vs Quantum Reaction Rates
Quantum Chemical Dynamics
Scattering off of a Barrier
Time-Independent Chemical Dynamics
Time-Independent Chemical Dynamics, In Depth
Pencasts
Scattering from a 1-D Barrier
Exercises
Chemical Reactions
Extra Credit
Chemical Reactions
Python
Python
Optional Feedback
Quick Survey
Molecular Rotations
The Quantum Rigid Rotor
Diatomic Molecule Hamiltonian
Vibrational and Rotational Interplay
The Rigid Rotor Approximation
Quantum Hamiltonian for a Diatomic Molecule
Angular Momentum Operator in Spherical Coordinates
Spherical Harmonics
Spherical Harmonics
Angular Momentum Operators and the Spherical Harmonics
Spherical Harmonics Visualization
Falstad
Evolution of a Gaussian Angular Distribution
Spectroscopy
Molecular Spectroscopy
Rotational Selection Rules
Molecular Rotation Spectra
Rotational-Vibrational Spectroscopy
The CO Molecule Spectrum
Pencasts
Classical Angular Momentum
Quantum Angular Momentum
Rotational Spectroscopy
Exercises
Molecular Rotations
Python
Python
Optional Feedback
Quick Survey
The Hydrogen Atom
A Historical Perspective
19th Century Spectroscopy
Classical Theory of The Hydrogen Atom
The Solvay Conference
Limitations of Bohr's Model
The Hydrogen Atom
Schrödinger Equation for the Hydrogen Atom
Energy Level Diagram
The Radial Eigenfunctions
Expectation Value of the Nuclear Distance
Full Hydrogen Eigenfunctions
Falstad
Magnetic Fields and the Hydrogen Atom
Classical Angular Momentum and Magnetic Fields
The Zeeman Interaction
Splitting of the Hydrogen Atom Energy Levels
Wrap-up
Pencasts
Classical Model of Hydrogen
The Quantum Hydrogen Atom
Exercises
The Hydrogen Atom
Harmonics and Complex Numbers
Python
Python
Optional Feedback
Quick Survey
Many-Electron Atoms
Introducing Spin
The Stern-Gerlach Experiment
Sulfur and Silver
Eigenfunctions of the Spin Operator
Hydrogen Atom Hamiltonian, including Spin
The Splitting of the Hydrogen Atom Spectrum
Understanding Helium
The Helium Atom
Singlet and Triplet States
The Very Poor Man's Approximation to the Helium Atom
First-order Perturbation Theory
Wrap-up
Pencasts
Electron Spin
The Helium Atom
The Very Poor Man's Helium
Exercises
Helium and Lithium
Extra Credit
The Harmonium Atom
Python
Python
Optional Feedback
Quick Survey
Diatomic Molecules
Parametrizing by Nuclear Distance
The Molecular Schrödinger Equation
The Born-Oppenheimer Approximation
The Nuclear Schrödinger Equation
Nuclear Separation Dependence of Energy
Starting Simple: The Hydrogen Molecular Ion
The Hydrogen Molecular Ion
Falstad
Linear Combination of Atomic Orbitals
Energy Expectation Value
Revisiting Separation Dependence of Energy
Pencasts
The Born-Oppenheimer Approximation
The Hydrogen Molecule Ion H2+
The Hydrogen Molecule Ion H2+ (Continued)
Exercises
The H3 Molecule
Python
Python
Optional Feedback
Quick Survey
Diatomic Molecules 2
Stepping it up: The Hydrogen Molecule
The Hydrogen Molecule
VPM/LCAO solution for H2
Poor Man's Energy Expectation
Very Poor Man's vs Poor Man's Approximations
Electron Configuration
Hydrogen Molecule Electron Configuration
Configuration Interaction
Configuration Interaction Matrix
Pencasts
The Hydrogen Molecule H2
The Hydrogen Molecule H2 (continued)
Exercises
Configuration Interaction
Python
Python
Optional Feedback
Quick Survey
Photophysics
Absorption and Relaxation I
Relaxation Processes
Photophysics Timescales
Light-Matter Interaction
The Frank-Condon Principle
Master Equation
Absorption and Relaxation II
Example: Vibrational Relaxation
Fluorescence
The Purcell Effect
Non-radiative Decay and Internal Conversion
Intersystem Crossing and Phosphorescence
Pencasts
Overview of Photophysics and Photochemistry
Radiative Transitions and the Franck-Condon Principle
Vibrational Relaxation
Fluorescence and Kasha's Rule
Exercises
Photophysics
No Python
No Python
Optional Feedback
Quick Survey
Dirac Notation and the Variational Principle
Dirac Notation
Brackets
Operators
Using Dirac Notation
Expansion and Projection
Infinite Spaces
More about Operators
Expectation Values and Matrix Elements
The Variational Principle
The Variational Principle
Variational Improvement on Poorman’s Helium
Hylleraas Wave Function
Pencasts
Dirac Notation
The Variational Principle
Exercises
Trial Wavefunctions
Extra Credit
Trial Wavefunctions
Python
Python
Optional Feedback
Quick Survey
Self-Consistent Field Theory
Hartree and Self-Consistent Fields
The Hartree Approximation
Hartree with Variation
The Self-Consistent Field Method
The Slater Determinant
The Slater Determinant
The Slater Determinant for Helium
Hartree Fock and Python
Wrap-up
Pencasts
The Hartree Approximation
The Hartree-Fock Approximation
Koopman's Theorem
Exercises
Self-Consistent Field Theory
Extra Credit
The Hartree Approximation
Python
Python
Optional Feedback
Quick Survey
Hartree-Fock and Perturbation Theory
Hartree-Fock
Hartree-Fock
Koopman's Theorem
Occupied and Unoccupied Orbitals
The Correlation Energy
Rayleigh-Schrödinger
Rayleigh Schrödinger Perturbation Theory
RSPT to Correct the Wavefunction
The Quartic Oscillator
Møller-Plesset
Møller-Plesset Perturbation Theory
Second-order Energy for MPPT
Data Table for BH3
Configuration Interaction Wavefunction
Limitations of Restricted H-F
Pencasts
Perturbation Theory
Perturbation Theory (continued)
Optional Pencasts
Coupled-Cluster Theory
The Bravais Lattice
Diffusion Monte-Carlo
The Reciprocal Lattice
Bloch's Theorem
Energy Bands
Energy Bands Part 2
Exercises
The Hartree-Fock Method
Python (Optional)
Python
Optional Feedback
Quick Survey
Wrap-up
Final Notes
Almost Done
Where to Go from Here?
Post-Course Survey
Post-Course Survey
Thank you!
Thank you!