Quantum Chemistry

  1. Exactly Solvable Quantum Systems
    1. Particle in a Box
      1. One-Dimensional Infinite Square Well
        1. Boundary Conditions
          1. Solution Method
            1. Quantized Energy Levels
              1. Wavefunctions and Normalization
                1. Nodes and Probability Distributions
                2. Finite Square Well
                  1. Bound States
                    1. Penetration into Barriers
                      1. Transcendental Equations
                      2. Multi-Dimensional Boxes
                        1. Two-Dimensional Box
                          1. Three-Dimensional Box
                            1. Separation of Variables
                              1. Degeneracy
                              2. Quantum Tunneling
                                1. Potential Barriers
                                  1. Transmission Coefficient
                                    1. Reflection Coefficient
                                      1. Tunneling Applications
                                    2. Harmonic Oscillator
                                      1. Classical Harmonic Motion
                                        1. Hooke's Law
                                          1. Potential Energy Function
                                            1. Classical Solutions
                                            2. Quantum Harmonic Oscillator
                                              1. Schrödinger Equation Setup
                                                1. Dimensionless Variables
                                                  1. Series Solution Method
                                                  2. Algebraic Solution
                                                    1. Ladder Operators
                                                      1. Creation and Annihilation Operators
                                                        1. Commutation Relations
                                                        2. Energy Levels and Wavefunctions
                                                          1. Quantized Energy Levels
                                                            1. Zero-Point Energy
                                                              1. Hermite Polynomials
                                                                1. Gaussian Envelope
                                                                2. Properties and Applications
                                                                  1. Classical Turning Points
                                                                    1. Probability Distributions
                                                                      1. Vibrational Spectroscopy
                                                                    2. Rigid Rotor Models
                                                                      1. Particle on a Ring
                                                                        1. Circular Motion
                                                                          1. Angular Momentum Quantization
                                                                            1. Energy Levels
                                                                              1. Wavefunctions
                                                                              2. Particle on a Sphere
                                                                                1. Spherical Coordinates
                                                                                  1. Angular Momentum in 3D
                                                                                    1. Spherical Harmonics
                                                                                    2. Spherical Harmonics
                                                                                      1. Mathematical Properties
                                                                                        1. Orthogonality Relations
                                                                                          1. Associated Legendre Polynomials
                                                                                            1. Visualization and Nodal Patterns
                                                                                            2. Angular Momentum Quantization
                                                                                              1. Quantum Numbers l and m
                                                                                                1. Magnitude and z-Component
                                                                                                  1. Vector Model
                                                                                                2. Hydrogen Atom
                                                                                                  1. Central Force Problem
                                                                                                    1. Coulomb Potential
                                                                                                      1. Separation in Spherical Coordinates
                                                                                                        1. Radial and Angular Parts
                                                                                                        2. Angular Solution
                                                                                                          1. Spherical Harmonics
                                                                                                            1. Angular Momentum Quantum Numbers
                                                                                                            2. Radial Solution
                                                                                                              1. Radial Equation
                                                                                                                1. Associated Laguerre Polynomials
                                                                                                                  1. Radial Wavefunctions
                                                                                                                  2. Complete Solution
                                                                                                                    1. Quantum Numbers n, l, m
                                                                                                                      1. Energy Levels
                                                                                                                        1. Degeneracy
                                                                                                                        2. Atomic Orbitals
                                                                                                                          1. s, p, d, f Orbitals
                                                                                                                            1. Orbital Shapes
                                                                                                                              1. Nodal Structure
                                                                                                                                1. Radial Distribution Functions

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                                                                                                                            2. Fundamental Postulates of Quantum Mechanics

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                                                                                                                            4. Approximation Methods