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 www.phys.uu.nl/~thooft/lectures/lieg07.pdf
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 ?