intermediate
321 lessons across two tracks.
Physics & Mechanics
1. Hilbert Spaces & Dirac Formalism
2. Operators, Eigenvalues & Spectral Theorem
3. The Postulates of Quantum Mechanics
4. Time Evolution & the Schrödinger Picture
5. The Harmonic Oscillator: Ladder Operators
6. Angular Momentum Theory
- Angular Momentum Operators
- Commutation Relations
- The Total Angular Momentum L²
- Raising and Lowering Operators L±
- Eigenvalues of L² and L_z
- Quantum Numbers ℓ and m
- Spherical Harmonics
- Orbital vs Spin Angular Momentum
- Matrix Representations
- Vector Model of Angular Momentum
- Expectation Values of Components
- Checkpoint: Angular Momentum Algebra
7. Spin-½ Systems & Pauli Algebra
8. Addition of Angular Momenta
9. The Hydrogen Atom in Depth
- The Coulomb Potential
- Separating Radial and Angular Parts
- The Radial Equation
- Energy Levels Revisited
- Radial Wavefunctions
- Degeneracy and Quantum Numbers
- Probability Densities and Orbitals
- Expectation of Radius ⟨r⟩
- Selection Rules for Transitions
- The Zeeman Effect (Intro)
- Fine Structure (Overview)
- Checkpoint: Hydrogen in Depth
10. Identical Particles & Exchange Symmetry
11. Time-Independent Perturbation Theory
- Why Perturbation Theory
- First-Order Energy Corrections
- First-Order State Corrections
- Second-Order Energy Corrections
- Degenerate Perturbation Theory
- The Stark Effect
- The Zeeman Effect (Perturbative)
- Fine Structure Corrections
- Validity of Perturbation Theory
- Two-Level Perturbation
- Anharmonic Oscillator
- Checkpoint: Perturb a System