#include "harmonic.h"
#include <vector>
using namespace std;

double harmonic::hermite(int k, double x) {
	double h0 = 1;
	if (k==0) return h0;
	double h1= 2*x;
	if (k==1) return h1;
	double h2=-2*h0+2*x*h1;
	if (k==2) return h2;
	for (int i=2; i<k; i++) {
		h0=h1;
		h1=h2;
		h2=-2*i*h0+2*x*h1;
	}
	return h2;
}


double harmonic::wav1d(int k, double x) {
	double fac=1; // 2^n * n!
	for (int i=1; i<(k+0.5); i++) {
		fac *= 2*i;
	}
	double norm = atan(1)*4; // (pi)
	double param = sqrt(mass*spring);
	norm = sqrt (param/norm);
	norm = sqrt(norm/fac);
	x *= sqrt(param);
	norm *= hermite(k,x);
	norm *= exp (-x*x/2);
	return norm;
}
	
double harmonic::secdiv(int k, double x) {
	double E = (k+0.5) * sqrt(spring/mass);
        double V=spring/2*x*x;
	double secdiv= -2*mass*(E-V);
	return secdiv;
}