void cauchy_lorentz()
{

  TH1* h1 = new TH1F( "h1", "Cauchy-Lorentz-Verteilung: x_{0}=0, #Gamma=1", 10, -5, 5 );
  h1->SetXTitle( "x" );
  h1->SetYTitle( "f(x;x_{0},#Gamma)" );
  h1->SetMaximum( 0.8 );
  h1->SetStats( 0 );
  h1->Draw();

  TF1* f = new TF1( "f", cauchy, -5, 5, 2 );
  f->SetParameters( 0, 1 );
  f->SetNpx( 1000 );
  f->Draw("same");


  gPad->SaveAs("cauchy_lorentz.pdf");
  
  TH1* h2 = new TH1F( "h2", "Cauchy-Lorentz-Verteilung: x_{0}=2, #Gamma=0.5", 10, -5, 5 );
  h2->SetXTitle( "x" );
  h2->SetYTitle( "f(x;x_{0},#Gamma)" );
  h2->SetMaximum( 0.8 );
  h2->SetStats( 0 );
  h2->Draw();

 f->SetParameters( 2, 0.5 );
 f->Draw("same");

  gPad->SaveAs("breit_wigner.pdf");

}

double cauchy( double* x, double* par )
{
  double val = x[0];
  double x0 = par[0];
  double Gam = par[1];

  return TMath::InvPi() * Gam/((val-x0)*(val-x0) + Gam*Gam);
}