Small library for setting up energy expressions for electronic systems
that can be used to derive differential equations via calculus of
variations. The mathematics are not tied to atomic systems (which are
spherically symmetrical), and most of the code in this library could
be used to derive equations for e.g. molecules. However, the
AbstractOrbital and SpinOrbital types are taken from the
AtomicLevels.jl
library at present.
When dealing with configurations of spin-orbitals, where all quantum numbers are specified, it is trivial to derive the energy expression. For e.g. configuration state functions (CSFs), which are spin-averaged linear combinations of multiple Slater determinants, the problem is much more involved and requires dealing with angular momentum coupling and tensor algebra. This library could be used as a basis for building such functionality.