hydrogen.h

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 *                                                                           *
 *                       / /   / /    __    \ \  / /                         *
 *                      / /__ / /   / _ \    \ \/ /                          *
 *                     /  ___  /   | |/_/    / /\ \                          *
 *                    / /   / /    \_\      / /  \ \                         *
 *                                                                           *
 *                         Jakub Benda (c) 2014                              *
 *                     Charles University in Prague                          *
 *                                                                           *
\* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

#ifndef HEX_HYDROGEN
#define HEX_HYDROGEN

#include <vector>

#include "special.h"

#define DEFAULT_LAMBDA      1

// Default maximal iteration count when searching for nodes of the wave functions.
#define DEFAULT_MAXSTEPS    1000

namespace Hydrogen
{
    
double P (unsigned n, unsigned l, double r);

double lastZeroBound (int n, int l);

double getBoundN (int n, int l);

double S (int n, int l, double r, double lambda = DEFAULT_LAMBDA);

double getBoundFar (int n, int l, double eps, int max_steps = DEFAULT_MAXSTEPS);

double getSturmFar (int n, int l, double lambda, double eps, int max_steps = DEFAULT_MAXSTEPS);

double F (double k, int l, double r, double sigma = special::constant::Nan);

double evalFreeStatePhase (double k, int l, double sigma = special::constant::Nan);

double evalFreeState_asy(double k, int l, double r, double sigma);

double getFreeAsyZero(double k, int l, double Sigma, double eps, int max_steps, int nzero);

double getFreeAsyTop(double k, int l, double Sigma, double eps, int max_steps, int ntop);

double getFreeFar(double k, int l, double Sigma = special::constant::Nan, double eps = 1e-10, int max_steps = DEFAULT_MAXSTEPS);

}
    
class HydrogenFunction : public RadialFunction<double>
{
public:
    
    HydrogenFunction(int n, int l)
        : n_(n), l_(l) {}
    
    inline double far (double eps = 1e-10, int max_steps = 1000) const
    {
        return Hydrogen::getBoundFar(n_,l_,eps,max_steps);
    };
    
    inline int n () const { return n_; }
    
    inline int l () const { return l_; }
    
    double operator() (double r) const;
    
    double getTurningPoint () const;
    
    inline bool operator== (HydrogenFunction const & psi) const
    {
        return n_ == psi.n_ and l_ == psi.l_;
    }
    
private:
    
    int n_;
    
    int l_;
};

#endif