In the numerical calculation of the eigenenergies of a polynomial Hamiltonian, 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 becomes more regular than the untruncated Hamiltonian, as reflected by the Berry–Robnik level spacing distribution.
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