The Anderson orthogonality theorem is a theorem in physics by the physicist P. W. Anderson.

It relates to the introduction of a magnetic impurity in a metal. When a magnetic impurity is introduced into a metal, the conduction electrons will tend to screen the potential ${\displaystyle V(r)}$ that the impurity creates. The N-electron ground state for the system when ${\displaystyle V(r)=0}$, which corresponds to the absence of the impurity and ${\displaystyle V(r)\neq 0}$, which corresponds to the introduction of the impurity are orthogonal in the thermodynamic limit ${\displaystyle N\to \infty }$.