Plot the Amplitude of a Hydrogen Atom.
Visualize the Amplitude of a Hydrogen Atom in the n = 2, l = 0, m = 0 state. Demonstrates how TH2F can be used in Quantum Mechanics.
The formula for Hydrogen in this energy state is $ \psi_{200} = \frac{1}{4\sqrt{2\pi}a_0 ^{\frac{3}{2}}}(2-\frac{\sqrt{x^2+y^2}}{a_0})e^{-\frac{\sqrt{x^2+y^2}}{2a_0}} $
Author: Advait Dhingra
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, April 17, 2024 at 11:11 AM.
Definition of a helper function:
%%cpp -d
#include <cmath>
double WaveFunction(double x, double y) {
double r = sqrt(x *x + y*y);
double w = (1/pow((4*sqrt(2*TMath::Pi())* 1), 1.5)) * (2 - (r / 1)*pow(TMath::E(), (-1 * r)/2)); // Wavefunction formula for psi 2,0,0
return w*w; // Amplitude
}
TH2F *h2D = new TH2F("Hydrogen Atom",
"Hydrogen in n = 2, l = 0, m = 0 state; Position in x direction; Position in y direction",
200, -10, 10, 200, -10, 10);
for (float i = -10; i < 10; i += 0.01) {
for (float j = -10; j < 10; j += 0.01) {
h2D->Fill(i, j, WaveFunction(i, j));
}
}
gStyle->SetPalette(kCividis);
gStyle->SetOptStat(0);
TCanvas *c1 = new TCanvas("c1", "Schroedinger's Hydrogen Atom", 750, 1500);
c1->Divide(1, 2);
auto c1_1 = c1->cd(1);
c1_1->SetRightMargin(0.14);
h2D->GetXaxis()->SetLabelSize(0.03);
h2D->GetYaxis()->SetLabelSize(0.03);
h2D->GetZaxis()->SetLabelSize(0.03);
h2D->SetContour(50);
h2D->Draw("colz");
TLatex *l = new TLatex(-10, -12.43, "The Electron is more likely to be found in the yellow areas and less likely to be found in the blue areas.");
l->SetTextFont(42);
l->SetTextSize(0.02);
l->Draw();
auto c1_2 = c1->cd(2);
c1_2->SetTheta(42.);
TH2D *h2Dc = (TH2D*)h2D->Clone();
h2Dc->SetTitle("3D view of probability amplitude;;");
h2Dc->Draw("surf2");
Draw all canvases
gROOT->GetListOfCanvases()->Draw()