An eigenstate of a quantum observable is a state which results from a measurement of that observable which has produced a precise value; and according to quantum theory this means that it is represented by a normalized eigenvector for the corresponding self-adjoint operator (whose eigenvalue is equal to the observed measurement value).

An eigenvector of an operator [math]A[/math] is a vector [math]\Psi[/math] for which [math]A\Psi=\lambda\Psi[/math] for some number [math]\lambda[/math] (which is called the corresponding eigenvalue).