Can one use Delta E.Delta t greater than or equal to h/4pi in quantum mechanics?

Answer

The principle of indeterminacy (Heisenberg) applies between position and momentum: one can only determine this – for a given particle – with inaccuracies Δx and Δp, such that Δx Δp>h/2π. In the simple case of a free particle (eg electron), its state is described by a wave that differs from zero only in a certain area Δx; that wave is then composed of waves, each of which has its own momentum, around an average momentum with spread Δp.
Every impulse is accompanied by an energy, so one can also consider that wave as a sum of waves with different energies, spread over ΔE.
The movement of the particle is then represented by the total wave moving in space, the time it takes for that wave to pass a certain point is called Δt. From the relationship between energy, momentum and velocity follows ΔE Δt >h/2π. In that sense, the relationship is therefore valid and provable.

There is a mathematical reason why the relation between E and t does not have the same generality as that between x and p: in quantum mechanics the latter are represented by operators, whose mutual relations (the “commutation rules”) give rise to the indeterminacy relations. Time, on the other hand, is a parameter and not an operator and thus one cannot adopt the proof of place-impulse for the energy-time relation.