# What is the definition of an eigenstate of a hermitian operator?

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 $A$ is a vector $\Psi$ for which $A\Psi=\lambda\Psi$ for some number $\lambda$ (which is called the corresponding eigenvalue).