HOW FAST CAN A QUANTUM STATE CHANGE WITH TIME

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.