  We consider the entanglement properties of free fermions in one dimension and
review an approach which relates the problem to the solution of a certain
differential equation. The single-particle eigenfunctions of the entanglement
Hamiltonian are then seen to be spheroidal functions or generalizations of
them. The analytical results for the eigenvalue spectrum agree with those
obtained by other methods. In the continuum case, there are close connections
to random matrix theory.
