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$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$ $\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$ $\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$ $\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$
A scheme to solve the time dependent Schr\"{o}dinger equation \begin{equation} \label{eq01} i\hbar \dd{t}\ket{\psi} = \hat{H} \ket{\psi} \end{equation} is described. The final solution will be presented in the form, see \eqref{eq14} \begin{equation} \ket{\psi t} = U(t, t_0) \ket{\psi t_0} \label{eq16} \end{equation}where
\begin{equation}\label{EQ16A} U(t, t_0) \ket{\psi t_0} = \exp\Big(\frac{-i H(t-t_0)}{\hbar}\Big)\end{equation}
