Category: Hydrogen Atom

#pragma once

class RadialWaveFunction
{
private:
	static double Factorial(int n);
	static double Laguerre(double rho, int n, int l);
public:
	static double R(double r, int Z, int n, int l);
};

#include <math.h>
#include "RadialWaveFunction.h"

double RadialWaveFunction::Factorial(int n)
{
	double factorial = 1.0;

	for (int i = 2; i <= n; i++)
		factorial *= i;

	return factorial;
}

double RadialWaveFunction::Laguerre(double rho, int n, int l)
{
	double sum = 0.0;

	for (int k = 0; k <= n - l - 1; k++)
	{
		double factor1 = pow(-1, k + 2 * l + 1);
		double factor2 = pow(Factorial(n + l), 2.0);
		double factor3 = pow(rho, k);
		double numer = factor1 * factor2 * factor3;
		double factor4 = Factorial(n - l - 1 - k);
		double factor5 = Factorial(2 * l + 1 + k);
		double factor6 = Factorial(k);
		double denom = factor4 * factor5 * factor6;

		sum += numer / denom;
	}

	return sum;
}

double RadialWaveFunction::R(double r, int Z, int n, int l)
{
	double rho = 2.0 * Z * r / n;
	double numer1 = pow(2.0 * Z / n, 3.0);
	double numer2 = Factorial(n - l - 1);
	double denom1 = Factorial(n + n);
	double denom2 = pow(Factorial(n + l), 3.0);
	double numer3 = -sqrt(numer1 * numer2 /
		(denom1 * denom2));
	double exp2 = exp(-0.5 * rho);
	double rhol = pow(rho, l);
	return numer3 * exp2 * rhol * Laguerre(rho, n, l);
}