Spin operators (S)

The spin operators need as a basis definition two lists of equal length. The \textit{up} list indexes the orbitals with spin up, the \textit{down} list indexes the orbitals with spin down. I will generally use the even numbers for spin down and the odd numbers for spin up. (note that this yields the same basis definition as used in the \textit{Mathematica} package of Quanty and thus is needed if one mixes both codes)

Example.Quanty

IndexDn = {0,2,4,6}
IndexUp = {1,3,5,7}