1.6 Hermitian Operators

1

What is the defining characteristic of a Hermitian operator?

2

What important properties have the eigenfunctions and eigenvalues of a Hermitian operator?

3

What does it mean that the eigenfunctions of a Hermitian operator form a complete set?

4

Give a non diagonal matrix and a corresponding set of orthonormal eigenvectors.

5

Give a set of eigenfunctions of the operator ${\rm i}{\rm d}/{\rm d}{x}$ that are orthonormal and periodic on the interval $0<x<2\pi$.