sudden approximation

The sudden approximation is the opposite extreme to the adiabatic theorem: it applies when a system's conditions change so quickly that the system has no time to react during the change. In the blink before anything can respond, the wavefunction is caught frozen in place — it is, for that instant, exactly the state it was in just before the change. The system is then released into a new situation while wearing its old clothes.

Although the state itself does not change at the moment of the jump, it is generally no longer a natural energy state of the new conditions. So afterwards it must be re-expressed as a blend of the new system's energy states, and the squared weights in that blend tell us the probability of finding the system in each new level. A state that was perfectly settled before can suddenly become a rich mixture, ready to evolve in ways it could not before.

This idea is the right tool for genuinely abrupt events. When an atomic nucleus suddenly changes its charge in a radioactive decay, the surrounding electrons are caught unprepared, and the sudden approximation predicts how often they are shaken up into excited states or even ejected. The criterion for 'sudden' is the mirror image of 'adiabatic': the change must be fast compared with the system's own natural timescales, the very condition under which slow following becomes impossible.