InhomogenousGreens.hpp

#pragma once
#include <vector>
class DiracSpinor;
 
namespace DiracODE {
 
//==============================================================================
 
//! @brief Solves inhomogeneous Dirac equation
/*! @details
\f[ (H_0 + v -\epsilon_a)F_a = S \f]
with `source' term, S. Solves for \f$\psi_\kappa\f$ with angular momentum kappa.
en = \f$\epsilon\f$ is given. Note sign of S.
Uses Green's method (see Method documentation).
*/
DiracSpinor solve_inhomog(const int kappa, const double en,
                          const std::vector<double> &v,
                          const std::vector<double> &H_mag, const double alpha,
                          const DiracSpinor &source,
                          const DiracSpinor *const VxFa = nullptr,
                          const DiracSpinor *const Fa0 = nullptr,
                          double zion = 1, double mass = 1.0);
 
//! @brief Solves inhomogeneous Dirac equation
/*! @details
As above. Overload to accept/overwrite solution to Fa. kappa is taken from Fa.
*/
void solve_inhomog(DiracSpinor &Fa, const double en,
                   const std::vector<double> &v,
                   const std::vector<double> &H_mag, const double alpha,
                   const DiracSpinor &source,
                   const DiracSpinor *const VxFa = nullptr,
                   const DiracSpinor *const Fa0 = nullptr, double zion = 1,
                   double mass = 1.0);
 
//! @brief Solves inhomogeneous Dirac equation
/*! @details
As above. Overload to accept/overwrite solution to Fa.
All these routines solve also for Fzero, Finf, which are solutions to
homogeneous equation  (H-en)Fa = 0 [reg @ origin, and infinity, respectively].
  - The first two throw these solutions away, the third keeps them (in some
cases they can be re-used)
  - These Spinors are solved internally and over-written, they don't need to be
solved first (i.e., they are out parameters, not in/out parameters)
*/
void solve_inhomog(DiracSpinor &Fa, DiracSpinor &Fzero, DiracSpinor &Finf,
                   const double en, const std::vector<double> &v,
                   const std::vector<double> &H_mag, const double alpha,
                   const DiracSpinor &source,
                   const DiracSpinor *const VxFa = nullptr,
                   const DiracSpinor *const Fa0 = nullptr, double zion = 1,
                   double mass = 1.0);
 
//==============================================================================
 
namespace Internal {
 
// Takes solution regular at infinity (Finf), and that regular at zero (Fzero),
// and the inhomogenous source term, Sr, to find particular solution, Fa.
void GreenSolution(DiracSpinor &Fa, const DiracSpinor &Finf,
                   const DiracSpinor &Fzero, const double alpha,
                   const DiracSpinor &Sr);
 
} // namespace Internal
} // namespace DiracODE