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I'm an undergraduate taking the basic quantum classes and on my own, I'm trying to wrap my mind around how symmetry and group theory applies in Q.M. and theoretical physics in general; it's coming along slowly but surely!

Can someone please explain why the ammonia molecule is said to exhibit SU(2) symmetry? I can't imagine how the two symmetric states of ammonia have anything to do with the group of 2x2 complex unitary matrices of det=1.

Thanks

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# SU(2) symmetry of the ammonia molecule?

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