= Dynamical phase
{title2=$\delta=-\hbar^{-1}\int E(t)\,dt$}
For an <energy eigenstate> with instantaneous <energy eigenvalue> $E(t)$, the <dynamical phase> is
$$
\delta(T)=-\frac{1}{\hbar}\int_0^T E(t)\,dt.
$$
It comes from the <Schrödinger equation> and depends on the time spent evolving. In an ideal cycle under the <adiabatic theorem>, a periodic choice of instantaneous <energy eigenstate> gives $|\Psi(T)\rangle=e^{i(\delta+\gamma)}|\Psi(0)\rangle$, with <Berry phase> $\gamma$.
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