  Some of the subtleties of the integrability of the elliptic quantum billiard
are discussed. A well known classical constant of the motion has in the quantum
case an ill-defined commutator with the Hamiltonian. It is shown how this
problem can be solved. A geometric picture is given revealing why levels of a
separable system cross. It is shown that the repulsions found by Ayant and
Arvieu are computational effects and that the method used by Traiber et al. is
related to the present picture which explains the crossings they find. An
asymptotic formula for the energy-levels is derived and it is found that the
statistical quantities of the spectrum P(s) and \Delta(L) have the form
expected for an integrable system.
