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|un> = |un-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.)