Standalone viewer · the orbital cube

Hydrogenic eigenstates ψ_nlm

Pick an atom and a state. Compose shells, build superpositions, or step through molecular orbitals. Every volume here is precomputed on a GPU, shipped to R2, and raymarched in your browser.

view

model

atom H · Hydrogen

render

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slice

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Fig. 01·Volume render

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01Atom118

Element

02Shellsoccupied

Toggle individual shells. Each renders in its own colour.

02Superposition0 states

Add hydrogenic eigenstates with complex coefficients. Phase wheel: hue = arg ψ, brightness = |ψ|². Each state evolves as e^−iE_nt.

Add basis state

Time

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Operators

Apply an operator to read its expectation value on the current Ψ.

02Molecule9

Hand-tabulated LCAO orbitals: σ / σ*, π / π*, sp³ bonds + lone pairs. Hover a molecule then pick which orbital to view.

Orbital

03Principaln

04Angularℓ

05Magneticm

06Render3 modes

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07Slicex y z

Cut the volume open along an axis to expose its interior. Drag to rotate the cut into view.

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n 2

Principal n

ℓ p

Angular ℓ

m 0

Magnetic m

shells —

Compose shells

Full electron density. Switch hydrogenic ↔ HF above.

mol H₂

Molecule

mo —

Orbital