// Calculate matrix element of a coulomb potential given the charges
// of the elements
public double coulombPotentialEnergy(matrix A, matrix B)
{
double epsilon_0 = 1; // Unit is set to 1 maight want to make static units
/* int N = problem.getNumberOfParticles() - 1; // For easier readability */
int N = problem.getNumberOfParticles();
double result = 0;
matrix inverse = new QRdecomposition(A + B).inverse();
// For every particle pair (only counting once) calculate interaction
List <Particle> particles = problem.getParticles();
matrix Uinv = problem.getUInverse();
for (int j = 0; j < N; j++)
{
for (int i = 0; i < j; i++)
{
double p_ij = 0;
for (int k = 0; k < N - 1; k++)
{
for (int l = 0; l < N - 1; l++)
{
double b_ijk = Uinv[i, k] - Uinv[j, k];
double b_ijl = Uinv[i, l] - Uinv[j, l];
p_ij += b_ijk * inverse[k, l] * b_ijl;
}
}
/* result += particles[i].getCharge() * particles[j].getCharge() / (4 * Math.PI * epsilon_0) * Math.Sqrt(2 / (p_ij * Math.PI)) * overlapElement(A,B); */
result += particles[i].getCharge() * particles[j].getCharge() * 2.0 / epsilon_0 * Math.Sqrt(1 / (p_ij * Math.PI * 2)) * overlapElement(A, B);
}
}
return(result);
}
// Generate a list of permutations taking distinguishable particles into
// account. That is protons and electrons won't be swapped
public List <Permutation> permutations()
{
// Generate List of List of indistinguishable particles
List <List <int> > listlist = new List <List <int> >();
List <int> tmplist = new List <int>();
Particle p = problem.getParticles()[0];
tmplist.Add(0);
for (int i = 1; i < nParticles; i++)
{
if (problem.getParticles()[i].equals(p))
{
tmplist.Add(i);
}
else
{
listlist.Add(new List <int>(tmplist));
tmplist = new List <int>();
tmplist.Add(i);
p = problem.getParticles()[i];
}
if (i == nParticles - 1)
{
listlist.Add(new List <int>(tmplist));
}
}
// Generate List of List of permutations
List <List <Permutation> > llp = new List <List <Permutation> >();
foreach (List <int> list in listlist)
{
List <Permutation> permu = new List <Permutation>();
permu.Add(new Permutation(list, 1, -1)); // Need to change last parameter if boson
llp.Add(Misc.permutations(permu));
}
// List containing all previous permutations
List <Permutation> lp = new List <Permutation>();
for (int i = llp.Count - 1; i > -1; i--)
{
List <Permutation> tmp = new List <Permutation>();
foreach (Permutation per in llp[i])
{
Permutation clone = per.Clone();
if (lp.Count == 0)
{
tmp.Add(clone);
}
foreach (Permutation peru in lp)
{
Permutation clone2 = per.Clone();
clone2.Append(peru);
tmp.Add(clone2);
}
}
lp = new List <Permutation>(tmp);
}
return(lp);
}
