Floquet theory

The set of Floquet (after Gaston Floquet ) makes a statement about the structure of the Fundamentalmatrizen a homogeneous linear ordinary differential equations with periodic coefficients matrix.

This sentence is in quantum mechanics application, where the eigenstates of a system with time- varying periodic potential are also called Floquet states. They correspond exactly to the periodic component of the fundamental solution.

The set of Floquet applied to spatially periodic potentials is known in quantum theory better known by the name of Bloch 's theorem. The eigenstates are called Bloch functions.

From a quantum mechanical point of view can represent the situation this way: An undisturbed system has defined eigenstates. By applying a periodic field, the eigenstates are energetically changed. Due to the periodicity of the field is now also the eigenstates change periodically. They are referred to as Floquet states. By example, a Fourier expansion of these states to work with these can be greatly simplified.

Formulation

Each fundamental matrix of the homogeneous linear differential equation system

With steady - periodic coefficient matrix can be in the form

Write wherein continuously differentiable and periodic and a constant matrix. Here denotes the matrix exponential. If one is satisfied with the fact that is - periodic, can be chosen real -valued.

The transformation

Executes the system of differential equations with constant coefficients in an on: