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
raising operator.
For the case of the
quantum harmonic oscillator, the creation 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 annihilation operator)