ABSTRACT
In this chapter, the authors derive some of the models in order to make more evident their connection with physical problems and (more important) their limitations as tools for understanding nature. They focus attention on the relevant elements for the description of the dynamics, exploring the systems following our (educated) intuition. The semi classical approach to lasers assumes that the electromagnetic field can be treated by way of Maxwell’s equations, while the material is described quantum mechanically. The original Duffing oscillator was introduced in relation to the single (spatial) mode vibrations of a beam subjected to external periodic forces. The model has been extensively used as a prototype of periodically forced systems thanks to its simplicity. The laser system is closely related to a Hamiltonian problem in which the period of the oscillations increases with the energy (this feature, however, is not as evident as the symmetries of the other problems).
