A mathematical operator in quantum mechanics denoted by the symbol a which, when operating on the nth eigenstate of a given particle's wave function produces the (n-1)th eigenstate of that function:

a|u_n> = |u_n-1>

Also referred to as the lowering operator. By definition,

a|u₀> = 0

For the case of the quantum harmonic oscillator, the annihilation operator takes the form:

a = (q + ∂/∂q)/ √2

where q=√(2πmw/h)x with x representing the displacement of the particle, m representing the mass, w the angular frequency and h Planck's constant.

(See also creation operator.)