Quantum Operators
Linear mathematical operators that act on a wave function to yield physical observables (such as position, momentum, or energy).
Governing formula
p̂ = -i ℏ ∇, x̂ = x, Ĥ = -(ℏ² / (2m)) ∇² + V(x)
SI unit
Varies by Observable
In depth
In quantum mechanics, every measurable physical quantity corresponds to a linear Hermitian operator. Operating on an eigenstate yields an eigenvalue equation  ψ = a ψ, where eigenvalue 'a' is a real measurable physical value.
Examples in the real world
Applying the momentum operator p̂ = -i ℏ (∂/∂x) to a plane wave function to extract particle momentum p = ℏ k.