Hermitian Operator

An operator is Hermitian if and only if the Adjoint of the operator is equal to itself.

Properties

• all eigenvalues of a Hermitian operator are real

• All eigenvectors of a Hermitian operator form an orthonormal basis

• Observable are usually some kind of Hermitian operator

The eigenvalues represent possible measurement outcomes. Orthonormal Eigenstate $\left\lvert \alpha \right\rangle$ mean that these are Definite value states