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}