New form of the time-energy uncertainty relation

A new form of the time-energy uncertainty principle is presented. It has the form τ ΔE≥3π$5^{1/2}$/25, where τ is the average lifetime of a decaying state, and ΔE is the energy spread of the state computed from Δ$E^2$=〈$E^2$〉-〈E${〉}^2$. The particular state for which the above relationship becomes an equality is identified, and it is proved that all other states give a greater τ ΔE product. This general result should have a wide range of applications.