[QUE/QM-24001]

An arbitrary quantum mechanical system is initially in the state $\vert{0}\rangle$. At time $t=0$ a perturbation of the form $H^\prime =H_0 \exp(-t/T)$ is swithced on. Show that at large times the probability of the system being in the state \(\vert{1}\rangle\) is given by $$ \frac{|\langle0\vert H_0\vert1\rangle|^2}{(\hbar/T)^2 + (\Delta E)^2} $$ where $\Delta E$ is the energy difference in the states of $\vert{0}\rangle$ and $\vert{1}\rangle$.