SEMICLASSICAL LIMIT FOR A TRUNCATED HAMILTON

In the numerical calculation of the eigenenergies of a polynomial Hami ltonian, the majority of the levels depend on the cutoff of the basis used. By analyzing the finite Hamiltonian matrix as corresponding to a classical ''Action Billiard'' we are able to explain several features of the full spectrum using semiclassical periodic orbit theory. There are a large number of low-period orbits which interfere at the higher energies contained in the billiard. In this range the billiard become s more regular than the untruncated Hamiltonian, as reflected by the B erry-Robnik level spacing distribution. (C) 1996 American Institute of Physics.