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In $L_2 (\mathbb{R}^d; \mathbb{C}^n)$, we consider a selfadjoint matrixstrongly elliptic second order differential operator $\mathcal{A}_\varepsilon$with periodic coefficients depending on $\mathbf{x}/\varepsilon$. We findapproximations of the exponential $e^{-i \tau \mathcal{A}_\varepsilon}$, $\tau\in \mathbb{R}$, for small $\varepsilon$ in the ($H^s \to L_2$)-operator normwith suitable $s$. The sharpness of the error estimates with respect to $\tau$is discussed. The results are applied to study the behavior of the solution$\mathbf{u}_\varepsilon$ of the Cauchy problem for the Schr\"{o}dinger-typeequation $i\partial_{\tau} \mathbf{u}_\varepsilon = \mathcal{A}_\varepsilon\mathbf{u}_\varepsilon + \mathbf{F}$.

Operator error estimates for homogenization of the nonstationary Schr\"odinger-type equations: dependence on time