Mandelstam–Tamm theorem

$t_{\perp }\ge \frac{\pi \hslash }{2\delta E}$, where:

• $H$ is the Hamiltonian describing the system
• $(\delta E{)}^2:=⟨\psi |H^2|\psi ⟩-(⟨\psi |H|\psi ⟩{)}^2$ is the system’s Energy Variance.
• $\hslash$ is planck’s constant.
• $t_{\perp }$ is the minimum time required for the system to evolve into an orthogonal state, i.e. $⟨\psi |{\psi }_{t_{\perp }}⟩=0$.