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QM texts seem to have many ways of motivating the angular momentum operators and deriving the l and m quantum numbers . But the connection between physical rotaions in 3 dim space and an operator in hilbert space that is called " angular momentum" is still somewhat unclear to me

I found a set of notes on Lie Groups in Physics by Nobel prize winner Veltman - that seems to be particualry clear explanation of irreducible reps of SO(3) and angluar momentum operatiors

see on page 10 of

He begins with discussion of general linear diffrential equations that have a set of solutioins . He then says that when a 3 dim rotation takes place a solution of the DE is then transformed into a linear mixture of other solutions

Is this true for all linear diffrential equations -?? or are these type of transformations amoung solutions in response to 3 dim rotations an assumption that is made about wavefunctions or about states in a Hilbert space as part of the assumptions of QM ?

THanks Len

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