Quantum Hydrogen Orbital

Rigorous quantum mechanical visualization of the hydrogen atom wavefunction ψ_nlm(r, θ, φ). Renders volumetric 3D electron probability density clouds, spherical harmonics Y_l^m lobes, nodal boundary surfaces, and complex phase transitions for physics and chemistry study.

Playground

60 FPS • Canvas 2D

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Live Parameters

Principal (n) 3

Principal quantum energy level n

Angular (l) 2

Orbital angular momentum quantum number (0=s, 1=p, 2=d, 3=f)

Mathematical Formulation

66 chars high

Analytical Equation

\psi_{nlm}(r,\theta,\phi) = R_{nl}(r) Y_l^m(\theta,\phi), \quad P(r,\theta,\phi) = |\psi_{nlm}|^2

Compact Formula

P = Math.pow(r*n, l) * Math.exp(-r*2) * Math.abs(Y_lm(theta, phi))

Renderer Logic

// Quantum Hydrogen Orbital Wavefunction
const radialProb = Math.pow(rNorm * quantumN, quantumL) * Math.exp(-rNorm * 2.2);
const angularFactor = quantumL === 1 ? Math.abs(Math.cos(theta)) * 1.8 : Math.abs(3*Math.cos(theta)**2 - 1);
const P = radialProb * angularFactor;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#quantum-mechanics #physics-study #schrodinger-equation #hydrogen-orbital #spherical-harmonics #3d-cloud

Author: Quantum Physics Core Target: 60 FPS

Quantum Hydrogen Orbital

Live Parameters

Mathematical Formulation

Mathematical Tags

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