Syllabus

  • Brief Review of Newtonian Mechanics.
    • Concepts of Velocity, Acceleration, Mass, Force, Conservation of Momentum, Conservation of Energy…
  • Lagrangian mechanics on R^n
    • Calculus of Variations
    • Lagrangian Mechanics
      • Action Fuctional
      • Euler-Lagrange Equations
      • Invariance under Coordinate changes
    • Generalized Forces and Momenta, Conservation of Energy
    • Noether’s Theorem, Part 1
    • Constraints and Lagrange Multipliers
    • Examples: Rigid body, Spinning Top, Free motion in curved space & Geodesics
  • Hamiltonian Mechanics on R^n
    • The Legendre Transform
    • Hamilton’s Equations
      • Invariance under Coordinate changes
    • Liouville’s Theorem
      • Poincaré’s recurrence Theorem
    • The Poisson bracket
    • Noether’s Theorem, Part 2
      • Lie Algebras part 1
      • Lie algebra of Vector fields
      • Lie algebra of Hamiltonian functions
    • Cyclic Coordinates
      • Example: Particle moving in a central potential
  • Path-Integral approach to quantum mechanics
    • Oscillatory Integrals
    • Double Slit Experiment
    • Path Integrals
      • Semi-Classical Limit
      • Wave Functions and Probability
      • Free Particle
      • Harmonic Oscillator
    • Perturbative Methods and Born Approximations
      • Scattering
  • Wave functions revisted
    • Hilbert Space
      • States
      • Bra-Ket notation
      • State Collapse and inner products
    • Measurements
      • Position measurement
      • Momentum measurement & Fourier Transform
      • Self adjoint operators as measurements
      • Heisenberg Uncertainty relations
  • The Schrodinger Equation
    • Equivalence with the path integral
    • Time independant Schrodinger Equation & Hamiltonian Operator
      • Eigenvalues & Energy states
      • The Free particle, Part 2
      • The Harmonic Oscillator, Part 2
    • Noether’s Theorem Part 3
    • Canonical Quantization of T^*M
      • Dirac’s Correspondence principal
© David Li-Bland 2014