A new form of the time-energy uncertainty principle is presented. It has the form {τ} {Δ}E{≥}3{π}51/2/25, where {τ} is the average lifetime of a decaying state, and {Δ}E is the energy spread of the state computed from {Δ}E²=〈E²〉-〈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} {Δ}E product. This general result should have a wide range of applications.
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Gislason et al. (1985) studied this question.