A mathematical

operator in

quantum mechanics denoted by the symbol

**a** which, when operating on the

*n*th

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|u**_{0}> = 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.)*