# Orbitals

The first example defines a basis. Note that this example does not produce output.

Orbitals.Quanty
-- Although Quanty is a many body code,
-- the basis set is defined by one particle
-- orbitals with spin or sites. These are the
-- "boxes" that either can contain an
-- electron or not.
-- These Fermionic modes (lets call them
-- spin-orbitals) can either be the Wannier
-- functions in a solid, molecular orbitals for a
-- molecule or atomic wave-functions for an atom.
-- We obtain these orbitals with the use of either
-- DFT or Hartree Fock.
-- A minimal definition of the basis set is given
-- by the total number of Fermionic modes
-- (site, spin, orbital, ...) and Bosonic modes
-- (phonon modes, ...).

-- Note that the current version needs NB=0.

NF = 6;
NB = 0;

-- The elements of the basis are labeled by a
-- number. In the case here (NF=6) there are
-- six spin-orbitals with the imaginative name
-- 0,1,2,3,4, and 5.
-- In order to create Operators on this basis we
-- can relate these spin-orbitals to shells
-- in this case we could for example create a
-- p-shell. The spin-orbitals then should be
-- related to states with ml=-1, ml=0, or ml=1 and
-- ms=-1/2 or ms=+1/2
-- This we can realize by grouping them. Several
-- standard operators that only have a meaning
-- for a given angular momentum shell will
-- recognize this format.
-- For a p-shell we could define

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

-- the code knows that a 3 fold degenerate shell
-- has l=1 and ml=-1, 0 and 1 are assigned to
-- them automatically

-- That's all for basis sets. We do not define the
-- number of electrons at this point. Note that the
-- code is written to deal with systems where one
-- has 10^100 of possible determinants. The only
-- reason one can do this is by never writing down
-- those determinants.