Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrasesThe wave function satisfies $psi n+1T = F psi nT $ where $F$ is t

The given equation specifies that the wave function $\psi$ at time $(n+1)T$ is equal to the Floquet operator $F$ acting on the wave function at time $nT$. Assuming $\hbar$ and $m$ are both equal to 1, the Floquet operator $F$ can be represented as the product of two exponential terms: a term acting on momentum space that describes free evolution and a term acting on coordinate space that represents the kick-driven potential term. The eigenstate $|\alpha \rangle$ and the eigenvalue $V_\alpha$ of the kick-driven term $cos^2\theta$ can be used to obtain the matrix element of the Floquet operator $F$ in the momentum basis $|n\rangle$. This matrix element can be computed using Equation (\ref{dcc}), which involves a sum over all eigenstates $\alpha$ and their corresponding eigenvalues $V_\alpha$, as well as the inner products $\langle m|\alpha \rangle$ and $\langle \alpha|n \rangle$. To determine the evolution of the system starting from an initial state $|\psi_0 \rangle$, we can calculate the state of the system after $N$ periods using the equation $|\psi_N \rangle = \hat{F}^N |\psi_0 \rangle$.