# On mathematics behind molecular orbital energies

When explaining the mathematics behind calculating molecular orbital energy , namely HOMO and LUMO energies, using quantum chemistry, Chainer Chemistry documentation states that

From mathematical viewpoint it requires a solution of an internal eigenvalue problem for a Hamiltonian matrix.

1. I have never heard of internal eigenvalue problem in mathematics. Is this a term specific to quantum chemistry and what it means?
2. Is the Hamiltonian matrix same as Kohn-Sham Hamiltonian?