$$\begin{array}{r}H(t)=\left(\begin{array}{cc}E& v(t)\\ v(t)& -E\end{array}\right)=\underset{H_0}{\underbrace{\left(\begin{array}{cc}E& 0\\ 0& E\end{array}\right)}}+\underset{H^{\prime }}{\underbrace{\left(\begin{array}{cc}0& v(t)\\ v(t)& -2E\end{array}\right)}}\end{array}$$