Related simulators
Continue with similar topics in this category — or all 65 in Chemistry.
2D Box: Eigenstates & Degeneracy
Particle in a 2-D rectangular infinite well: ψ_{n_x,n_y} ∝ sin(n_xπx/L_x)sin(n_yπy/L_y), E ∝ (n_x/L_x)² + (n_y/L_y)². Toggle a square box (L_x = L_y) to expose the (n_x, n_y) ↔ (n_y, n_x) accidental degeneracy and watch the doublets split as the box deforms.
Particle in a 1D Box
Superposition of n=1 and n=2: time evolution of |Ψ|² and ⟨E⟩ (model units).
Coherent State |α⟩ in a Harmonic Oscillator
Animated Gaussian wavefunction of a coherent state |α⟩ in a 1-D harmonic well: rigid σ = 1/√2 packet whose centroid traces the classical orbit ⟨x⟩(t) = √2|α|cos(ωt − φ_α). Side-by-side phase space, |ψ(x,t)|², and ⟨x⟩(t) trace.
WKB / Bohr–Sommerfeld Quantization
Semiclassical bound-state energies for arbitrary V(x): harmonic, quartic, Morse, double-well, asymmetric and square wells. Bisection on the action ∫√(2m(E−V))dx = (n+½)πℏ gives the WKB ladder; compare with the exact harmonic ladder ℏω(n+½).
Anderson Localization (1D Tight-Binding)
Random onsite disorder W on a 1-D chain: diagonalize H, plot |ψ|² eigenstates, IPR vs energy, and localization length estimates (RMS and exponential fit).
Hydrogen |ψ|² (xz slice)
Coulomb hydrogen Z=1: |R_nl|² × |Y_lm|² colormap in the xz plane for textbook n,l states.