Interactive companions for an undergraduate quantum mechanics course. Pick the quantum numbers, watch the wavefunctions, probability densities, and orbital shapes update in real time. Everything is computed in your browser from the exact analytic eigenfunctions.
The infinite square well in 1D and 2D, two non-interacting particles in 1D, and two interacting particles: energy ladders with degeneracy, wavefunctions, and correlation.
Angular momentumThe planar-rotor states Φm(φ) = eimφ/√(2π): the m² energy ladder with ±m degeneracy, traveling vs standing waves, and a 3D wave around the ring.
1D bound statesHermite eigenfunctions drawn on their energy levels inside the parabola, with |ψn|² and the classical probability for the quantum→classical limit.
Angular momentumThe spherical-harmonic "balloons" of the rigid rotor, the Θ (Legendre) and Φ (ring) building blocks, and the (2ℓ+1)-fold degenerate energy ladder.
Central potentialRadial Laguerre functions Rnℓ(r), angular harmonics Yℓm split into Legendre × ring parts, and the full 3D orbital cloud with a complex ⇄ real-orbital toggle.
The chemical bondLCAO-MO for the one-electron ion H₂⁺: the bonding Σg and antibonding Σu* orbitals, MO diagram, and exact binding curve — then add a second electron to make H₂ (bond order, and the deeper two-electron curve).
Diatomic moleculesThe molecular-orbital shapes of heavier diatomics: σ and π combinations of 2s and 2p atomic orbitals, as 3-D boundary surfaces — bonding vs antibonding, gerade vs ungerade (note π bonding is u, opposite to σ).