Classical Anharmmonic Oscillator

The Lorentz model of the atom, which treats the atom as a harmonic oscillator, is known to provide a very good description of the linear optical properties of atomic vapors and of nonmetallic solids.  The model is extended by allowing the possibility of a nonlinearity in the restoring force exerted on the electron.  This additional non-linear force may or not break inversion symmetry, see figure below.

Anharmonic oscillator: with broken inversion symmetry (left) and with inversion symmetry (right)

The student should write a Python code that first integrates the standard
harmonic oscillator equation, and compare the result with the analytic solution.
Then he will include the non-linear corrections and compare the response functions with the one calculated in the Boyd book[3] in both the cases the one with or without inversion symmetry.


  1. Lorentz model and its applications
  2. How to Solve the Classical Harmonic Oscillator
  3. Classical anharmonic oscillator (Nonlinear Optics, Robert W. Boyd)
  4. Python Scripting for Computational Science
  5. Solving the Harmonic Oscillator Equations