I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days.

**Floquet theorem:**

Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The Floquet theorem says the solution to the Schrödinger equation will have the form

$$\psi(r,t)=e^{-i\varepsilon t}u(r,t)\ ,$$

where u(r,t) is a function periodic in time.

We can rewrite the Schrödinger equation as

$$\mathscr{H}u(r,t)=[H(t)-\mathrm{i}\hbar\frac{\partial}{\partial t}]u(r,t)=\varepsilon u(r,t)\ ,$$

the $\mathscr{H}$ can be thought as a Hermitian operator in the Hilbert space $\mathcal{R}+\mathcal{T}$, where $\mathcal{T}$ is a Hilbert space with all square integrable periodic functions with periodicity $\tau$. Then the above equation can be thought analogy to the stationary Schrödinger equation, with the real eigenvalue $\varepsilon$ defined as Floquet quasienergy.

My question is, since in stationary Schrödinger equation, we have continuous and discrete spectrum. How about floquet quasienergy?

Another thing is, is this a measurable quantity? If it is, in what sense it is measurable? (I mean, in the stationary case, the eigenenergy difference is a gauge invariant quantity, what about quasienergy?)

This post imported from StackExchange Physics at 2014-10-07 10:52 (UTC), posted by SE-user luming