On Wednesday, February 4, 2015 at 12:41:45 AM UTC+1, Aaron Meurer wrote:
>
>
> But do they actually use summation convention, as if i=0.5..2.5 meant i = 
> 0.5, 1.5, 2.5?
>

A spin state is usually represented by an N-dim vector, upon which act NxN 
matrices. The energies associated with these N entries correspond to N/2 to 
-N/2 times the reduced Planck constant. Sometimes, especially in the 
bra-ket notation, instead of using integers, one just uses the 
multiplication factor to the reduced Planck constant for the energies of 
those states as index, which may also appear in a sum. There are negative 
values, and if N is odd, they are half-integer.

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