More from Chemistry
Other simulators in this category — or see all 62.
Kronig–Penney Bands & Brillouin Zone
Periodic δ-comb model of a 1-D crystal: cos(ka) = cos(qa) + (P/qa) sin(qa). Find allowed energy bands and forbidden gaps from the |·|≤1 corridor, then watch each band fold into the first Brillouin zone k ∈ ±π/a. Free-electron parabola overlaid for reference.
Phonon Dispersion: 1-D Mass–Spring Chain
Monoatomic ω = 2√(K/m)|sin(ka/2)| or diatomic acoustic/optical branches from alternating masses; ω(k) and group velocity v_g = dω/dk in the first Brillouin zone with animated lattice snapshot.
Debye vs Einstein Heat Capacity
Molar C_V(T): Debye integral → T³ law at low T and 3R Dulong–Petit at high T; compare with Einstein single-frequency model and toggle curves on one plot.
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).
Bloch Oscillations & Wannier–Stark Ladder
1-D tight-binding electron in uniform field E: semiclassical k(t), Bloch-periodic x(t), and finite-chain Wannier–Stark ladder with spacing ≈ eEa.
Graphene Tight-Binding Band Structure
Honeycomb π tight binding: E(k) along Γ–M–K–Γ, Dirac cones at K and K′ when Δ=0, gap 2Δ from sublattice stagger, and a Brillouin-zone energy map.