atomec-project/atoMEC

Boundary conditions at leftmost gridpoint `x0`

timcallow opened this issue · 1 comments

Currently, the boundary condition applied at the LHS grid-point forces the (transformed) orbitals to be exactly zero. This is not strictly correct, in particular when we have l=0 angular quantum number.

This doesn't yet seem to be having an adverse impact on the computation of observables, but it would be interesting to see the impact of applying the correct boundary conditions. In the current Numerov diagonalization scheme, this would involve appropriate changes to the hamiltonian matrix in the top LH corner.

See the extract from Eli's thesis for the correct constraints (of course, our grid is just a log grid, we have no dependence on atomic number Z.)

Screenshot from 2021-08-05 13-03-51

Closing this because the evidence from many calculations suggests there is no impact in changing the left-hand boundary condition