Approximation of Schr{ö}dinger Unitary Groups of Operators by Particular Projection Methods
For researchers in quantum dynamics and operator theory, this work offers a theoretical framework for approximating unitary groups, but it is incremental as it applies known projection techniques with specific adaptations.
The paper develops projection methods to approximate unitary groups e^{-itH} for Hamiltonians in discretizable Hilbert spaces, providing theoretical interrelations and numerical estimates to validate the approach.
In this paper we work with the approximation of unitary groups of operators of the form $e^{-itH}$ where $H\in\mathscr{L}(\mathcal{H})$ is the Hamiltonian of a given quantum dynamical system modeled in the discretizable Hilbert space $\mathcal{H}=\mathcal{H}(G)$, to perform such approximations we implement some techniques from operator theory that we name particular projection methods by compatibility with quantum theory conventions. Once particular representations are defined we study the interelation between some of them properties with the original operators that they mimic. In the end some estimates for numerical implementation are presented to verify the theoretical discussion.