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View Code? Open in Web Editor NEWJust-in-time-compiled solver for the radial Shrödinger equation using the calculable R-Matrix method on a Lagrange-Legendre mesh
License: BSD 3-Clause "New" or "Revised" License
Just-in-time-compiled solver for the radial Shrödinger equation using the calculable R-Matrix method on a Lagrange-Legendre mesh
License: BSD 3-Clause "New" or "Revised" License
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
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
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