Abstract:
The states of a system of $N$ harmonic oscillators with fixed total number of quanta are decomposed with respect to bases of irreducible representations of $SU(2)$. The previously introduced basis [1] is a basis with the highest dimensionality in this decomposition. For the
case of three harmonic oscillators, the operators and a discrete basis of a representation
of the noncompact group $SU(1,1)$ are constructed. Bargmann's representation is considered
for these states.
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