In reviewing the derivation of the quantization of angular momentum-like operators from their commutation relations, I noticed that there is nothing a priori from which you can deduce the degeneracy of the eigenstates. While this is not a problem for angular momentum, in which other constraints come into play, it seems to me that it might be a problem for spin. Is it possible to deduce the dimensionality from the spin commutation relations alone? Or must one postulate it?(adsbygoogle = window.adsbygoogle || []).push({});

For example, I know from the commutation relations that for an electron, any non-trivial eigenstates of Sz have eigenvalues +1/2 or -1/2. But how do I know that there are only two degrees of freedom? That is, how do I know that there's no degeneracy in the m eigenvalues?

On a somewhat unrelated note, does anyone know of any good references on rigged Hilbert spaces? Thanks.

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# Spin degeneracy

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