Lower and upper bounds are derived for the decay and transitions of qu
antum states, evolving under a time-dependent Hamiltonian, in terms of
the energy uncertainty of the initial and final state. The bounds are
simultaneously a rigorous version of Fermi's golden rule and of the t
ime-energy uncertainty relation. They are sharp, refer to short times,
and are compared with recent long-time results for time-independent H
amiltonians. Illustrations for tunneling systems, laser-driven process
es, and neutron interferometry in time-dependent magnetic fields are g
iven.