Hydrogen Electron Standing Waves

|1, 0, 0⟩

E₁ = −13.6 eV

1s ground state — spherically symmetric, no nodes

The electron is a standing wave — ψ(r,θ,φ) = R_nℓ(r) · Y_ℓm(θ,φ). Only states where the wavefunction closes on itself (integer wavelengths around the orbit) are allowed — this is why energy is quantized.

The bottom panel shows the radial probability density r²|R(r)|² — the likelihood of finding the electron at distance r.

Hydrogen Standing Waves