beykyle / jitr Goto Github PK

This is simply matrix-vector reduction, see Baye 2015 Eq. 2.85 and Dexcouvemont and Baye, 2010 section 3.8

In particular, to get the distorted wave coefficients in the Lagrange mesh basis involves first getting the S-matrix, using that to get the derivative boundary conditions, and then finally solving a second system to get the coefficients. Both systems being solved have the same, potentially non-Hermitian (for complex potentials), operator, but different source terms.

It may be faster to first store a factorization of the matrix (e.g. Chebyshev), and then solve both systems using it.

See Dexcouvemont and Baye, 2010 section 3.9

https://docs.sympy.org/latest/modules/physics/wigner.html this library will probably be useful for this

This involves

• evaluating Whittaker functions for the asymptotic behavior of closed channels (Descouvemont 2016 Eq. 4)
• adding a finite B value for closed channels (Descouvemont 2016 Eq. 9)
• reduce the S-matrix solve to be just over open channels (Descouvemont 2016 Eq. 16-17)

in examples/nonlocal.py

Does not agree with analytic solution given in section 6.1 of Baye 2015

Also discussed here: https://www.sciencedirect.com/science/article/pii/S0375947402010400

This involves adding a new solver using a Lagrange-Laguerre basis, see Baye 2015 section 3.3, which will be similar to the current one but with domain [0,inf]

An iterative, self-consistent search for bound state energies would also be useful