Generalized energy–time uncertainty relation

Starting with the Schrödinger universal uncertainty relations for arbitrary observables, we propose a generalization of the time uncertainty concept introduced by Mandelshtam and Tamm making it invariant with respect to the choice of observables and free of singularities. We show that for coherent states, the quantity introduced can be interpreted as the variance of the inverse effective frequency of the microsystem. This allows treating the generalized energy–time uncertainty relations similarly to the energy–inverse temperature uncertainty relations in statistical thermodynamics.