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Overview
Chapters
1. Intro to Quantum Mechanics
Why Quantum mechanics
The need for quantization
Photoelectric effect
Atomic spectra
Wave-particle duality
DEMO: Black Body radiation
DEMO: Visualizing complex numbers
2. Waves and wave equation
Waves
Wave equation
DEMO: Visualizing waves
DEMO: Bonus challenge
3. Schordinger Equation
Schrödinger Equation
Wave function
Particle in a Box
Applications of Particle in a Box Model
Postulates
P1 Characteristics of Quantum Wavefunctions
P2 Operators
P3-4 Eigenvalues and Expectation
P5 Time dependence
Fourier Transforms and Quantum Mechanics
DEMO: Particle in a box
DEMO: Quantum Waves
DEMO: Bonus challenge
4. Model systems
Molecular degrees of freedom
Classical Harmonic Oscillator
Quantum harmonic oscillator
Molecular Vibrations
Angular momentum
Rigid Rotor
5. Hydrogen Atom
Hydrogenlike atoms
Atomic orbitals
Spin
DEMO: H wavefunctions
Bonus: Atomic Orbitals
6. Approximations
Perturbation Method
Variational Method
Linear Variational Method
DEMO: Pertrubation Theory
DEMO: Solving QM problems with Variational method
7. Multielectron atoms
Helium atom
Multi-electron atoms
Angular momentum of many-electron atoms
Hartree-Fock
8. Molecules
BO approximation
The hydrogen molecule ion
Electronic structure of polyatomic molecules
Huckel molecular orbital theory
Dipole moments and ionic bonding
Intermolecular forces
DEMO: Solving
\(H^{+}_2\)
via Variational Method
DEMO: HF calculations on small organic molecules by PySCF
A. Math
Integrals
Differentiation
Complex numbers
Linear Algebra 1: Basics
Linear Algebra 2: Enter The Matrix
Linear Algebra 3: Inner products
Application: Hopfield Neural Networks
B. Practice Problems
Practice Problems for Exam 2
Extra stuff
Equation sheet
Python
Python3
NumPy
Plotting
Sympy
Index
