Ladder operators allow quantum mechanical operators to be incremented or decremented by one or more quantum states. Such operators exist whenever the commutator Eric Weisstein's World of Math of two operators has the form
where is the momentum operator, is the position operator, and is h-bar. Expanding the operator equation gives
where the creation operator is
and the annihilation operator is
with m the mass of the particle and its angular frequency.
Annihilation Operator, Creation Operator, Momentum Operator, Position Operator
