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In this paper we work with the approximation of unitary groups of operatorsof the form $e^{-itH}$ where $H\in\mathscr{L}(\mathcal{H})$ is the Hamiltonianof a given quantum dynamical system modeled in the discretizable Hilbert space$\mathcal{H}=\mathcal{H}(G)$, to perform such approximations we implement sometechniques from operator theory that we name particular projection methods bycompatibility with quantum theory conventions. Once particular representationsare defined we study the interelation between some of them properties with theoriginal operators that they mimic. In the end some estimates for numericalimplementation are presented to verify the theoretical discussion.

Approximation of Schr{\"o}dinger Unitary Groups of Operators by Particular Projection Methods