Abstract
For each irreducible representation [λ] ofU(n), a discrete irreducible unitary representation ofSp(n) is constructed for which the oscillator Hamiltonian is bounded from below with its ground-state eigenspace transforming according to [λ] underU(n). A basis of eigenstates for the harmonic oscillator is determined and the action of the Lie algebrasp(n) on that basis explicitly given. Connections with the Bohr collective vibrational model are established.
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