[QUE/QM-07015]

$\newcommand{\ket}[1]{|#1\rangle}$

{Let \(\ket{E_1},\ket{E_2}\) denote normalized energy eigenstates with energies \(E_1\ne E_2\). Let \(\psi\) be the superposition  \[ \ket{\psi} = a\ket{E_1} + b\ket{E_2},\]  \(a,b\) are complex constants. Obtain an expression for the uncertainty in energy \((\Delta E)_\psi\)in the state \(\ket{\psi}\). Find all conditions so that \(\Delta E\) may be zero, and interpret the answers you get.}