Tentative Syllabus: Quantum Mechanics

1. Introduction
   1. Breakdown of classical mechanics
   2. Partice wave duality
   3. The probabalistic nature of nature
      1. Probability & probability density
      2. The wave function
      3. Expectation values
   4. Fourier Transforms
   5. Dirac Delta Function
   6. Gaussian Integrals
   7. Schrödingers Equation
2. Schrödinger's equation in one dimension
   1. Free Particle
   2. Infinite Square Well
   3. Particle in a Box
   4. Delta Function Potential
   5. Quantum Harmonic Oscillator
      1. Hermite Polynomials: H_n
      2. Raising & lowering (ladder) operators
3. Schrödinger's equation in three dimensions
   1. Particle in a 3D infinite well
   2. Spherical Coordinates
   3. Separation of variables
   4. Angular Equations
      1. Legendre Polynomials: P_l
      2. Associated Legendre Functions: P_l^m
      3. Spherical Harmonics: Y_l^m
   5. Radial Equations
   6. Orbital Angular Momentum
      1. Angular Momentum Operators
      2. Commutations Relations
      3. Raising & Lowering (ladder) Operators
   7. Intrinsic Spin
4. Identical Particles
   1. Two Partile systems
   2. Spherical Coordinates
   3. Separation of variables
   4. Angular Equations