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Prompted by recent results on Susy-U(N)-invariant quantum mechanics in thelarge N limit by Veneziano and Wosiek, we have examined the planar spectrum inthe full Hilbert space of U(N)-invariant states built on the Fock vacuum byapplying any U(N)-invariant combinations of creation-operators. We presentresults about 1) the supersymmetric model in the bosonic sector, 2) thestandard quartic Hamiltonian. This latter is useful to check our techniquesagainst the exact result of Brezin et al. The SuSy case is where Fock spacemethods prove to be the most efficient: it turns out that the problem isseparable and the exact planar spectrum can be expressed in terms of thesingle-trace spectrum. In the case of the anharmonic oscillator, on the otherhand, the Fock space analysis is quite cumbersome due to the presence of largeoff-diagonal O(N) terms coupling subspaces with different number of traces;these terms should be absorbed before taking the planar limit and recoveringthe known planar spectrum. We give analytical and numerical evidence that goodqualitative information on the spectrum can be obtained this way.Comment: 17 pages, 4 figures, uses youngtab.sty. Final versio

The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case