Hydrogen Atom: 1s Orbital

Overview

This project simulates the electron probability distribution of a hydrogen atom’s 1s orbital using Monte Carlo sampling. The data is streamed over UDP for real-time visualization in Serial Studio.

This is not a classical orbit model. Instead, it displays probabilistic electron positions derived from quantum mechanics, visualized as a dynamic 3D cloud.

Note: This project uses features available only under a paid license. Visit serial-studio.com for more information.

Simulation Model

The electron's radial distance from the nucleus, denoted by r, is sampled using the probability distribution for the 1s orbital:

$$ P(r) \propto r^2 \cdot e^{-2r / a_0} $$

Where:

• $$r$$: Radial distance from the nucleus.
• $$a_0$$: Bohr radius (normalized to 1.0).

Electron positions are computed in spherical coordinates, then converted to Cartesian $$(x, y, z)$$.

Project Features

• Real-time 3D visualization of the electron cloud.
• Plot of probability density along the X-axis.
• 1 kHz data stream for smooth visual updates.

Data Format

Each UDP frame contains five comma-separated values:

x, y, z, psi2, r

Where:

• x, y, z: Electron position in Cartesian coordinates (in units of $$a_0$$).
• psi2: Probability density $$\psi^2(r) = |\psi(r)|^2$$.
• r: Radial distance from the nucleus (in units of $$a_0$$).

Example:
-0.283291,0.453772,0.125448,0.038142,0.621987

How to Run

1. Run the simulation:

   python3 hydrogen.py

2. In Serial Studio:

   • Open the Hydrogen.ssproj project file.
   • Set the input source to UDP, port 9000.
   • Click Connect.

Serial Studio Visualizations

• 3D Plot: Displays the real-time electron cloud in space.
• XY Plot: Plots $$psi^2$$ vs. $$x$$, showing spatial density.

Files Included

• hydrogen.py: Python script for simulation and UDP streaming.
• Hydrogen.ssproj: Serial Studio project file.
• README.md: Project documentation.
• doc/screenshot.png: Screenshot of the visualization.

Notes

• This simulation does not numerically solve the Schrödinger equation; it samples from the known analytical 1s solution.
• All spatial values are in normalized Bohr units $$a_0 = 1$$.