Eigenvalues and eigen vectors of Hermitean operators are defined as
for matrices, i.e., where there is a matrix-vector product we get an
operator acting on a function, and the eigenvalue/function equation becomes
f (x) = onf (x),
(8.5)
where on is a number (the ``eigenvalue'' )and f (x) is the
``eigenfunction''.
A list of important properties of the eigenvalue-eigenfunction pairs
for Hermitean operators are:
1.
The eigenvalues of an Hermitean operator are all real.
2.
The eigenfunctions for different eigenvalues are orthogonal.