Hydrogen Cloud

In the solution to the Schrödinger equation, which is non-relativistic, hydrogen-like atomic orbitals are eigenfunctions of the one-electron angular momentum operator \(L\) and its \(z\) component \(L_z\)​. A hydrogen-like atomic orbital is uniquely identified by the values of the principal quantum number \(n\), the angular momentum quantum number \(l\), and the magnetic quantum number \(m_l\).

How to interact: The visualization renders a 3D probability cloud using ray marching. The foreground canvas is interactive - you can rotate the view to see the orbital from different angles.

What you're seeing:

• Brighter regions show higher probability of finding the electron
• The shape is determined by quantum numbers n, l, and m
• Different orbitals (s, p, d, f) have distinct shapes
• The visualization solves the Schrödinger equation for the hydrogen atom

These quantum mechanical wavefunctions are the foundation of chemistry - they determine how atoms bond and interact with each other.