Q.No:1 CSIR-Dec-2014
Let \(\psi_1\) and \(\psi_2\) denote the normalized eigenstates of a particle with energy eigenvalues \(E_1\) and \(E_2\) respectively, with \(E_2>E_1\). At time \(t=0\) the particle is prepared in a state
\[
\Psi(t=0)=\frac{1}{\sqrt{2}}(\psi_1+\psi_2).
\]
The shortest time \(T\) at which \(\Psi(t=T)\) will be orthogonal to \(\Psi(t=0)\) is
(1) \(\frac{2\hbar \pi}{(E_2-E_1)}\)
(2) \(\frac{\hbar \pi}{(E_2-E_1)}\)
(3) \(\frac{\hbar \pi}{2(E_2-E_1)}\)
(4) \(\frac{\hbar \pi}{4(E_2-E_1)}\)