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I'm confused by a sentence in a set of lecture notes I have on quantum mechanics. In it, it is assumed there is some representation [itex]\pi[/itex] of [itex]SO(3)[/itex] on a Hilbert space. This representation is assumed to be irreducible and unitary.

It is then said that the operators [itex]J_i[/itex], which are said to be the infinitesimal generators of the rotation group satisfying [itex][J_i,J_j]=i \epsilon_{ijk}[/itex], are Hermitian as a consequence of the unitarity of this representation.

This confuses me. Shouldn't they say that the operators [itex]\pi (J_i)[/itex] are Hermitian? Are they writing [itex]J_i[/itex] for both the infinitesimal generators of the group and the operators they are mapped to?

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# Unitarity angular momentum operators

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