Chemistry
Molecules, periodic table, reactions, pH scale, and titration
- NewSchool
Hückel π-MO (Butadiene & Benzene)
Secular matrix H = αI + βA; eigen-energies and LCAO maps on the π skeleton.
- NewSchool
MO Diagram: Homonuclear Diatomics (H₂–O₂)
σ/π ladder with Li–N vs O ordering; bond order from valence MOs; O₂ π* unpaired → paramagnetism.
- NewUniversity / research
Wigner Function (Coherent vs Squeezed)
Phase-space quasi-probability W(x, p) for a single-mode Gaussian quantum state: coherent |α⟩, displaced-squeezed D(α)S(ξ)|0⟩, and thermal…
- NewUniversity / research
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…
- NewUniversity / research
WKB / Bohr–Sommerfeld Quantization
Semiclassical bound-state energies for arbitrary V(x): harmonic, quartic, Morse, double-well, asymmetric and square wells. Bisection on t…
- NewUniversity / research
Qubit Decoherence: Lindblad / T₁ T₂
Two-level Bloch master equation in the rotating frame with drive Ω, detuning Δ, T₁ relaxation and T₂ transverse decay. The Bloch vector s…
- NewUniversity / research
Ramsey Fringes (Atomic Clock)
Separated-oscillating-fields sequence π/2 — τ — π/2 with detuning Δ and coherence T₂. Sweep τ or Δ to see P(|1⟩) = ½(1 − cosΔτ · e^{−τ/T₂…
- NewUniversity / research
CHSH Bell Inequality Test
Monte-Carlo of the singlet state |Ψ⁻⟩ at four measurement angles (a, a′, b, b′): the running estimate Ŝ approaches the Tsirelson bound 2√…
- NewUniversity / research
Hong–Ou–Mandel Two-Photon Dip
Two indistinguishable photons enter opposite ports of a 50/50 beam splitter and bunch into the same output: coincidence probability P_c(δ…
- NewUniversity / research
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 c…
- NewUniversity / research
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 t…
- NewUniversity / research
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 cur…
- NewUniversity / research
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…
- NewUniversity / research
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 spacin…
- NewUniversity / research
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 ene…
- NewUniversity / research
Quantum Hall Edge States & σ_xy Plateaus
Integer QHE: chiral edge channels and skipping orbits in a Hall bar, filled Landau levels vs μ, and quantized Hall conductance plateaus σ…
- NewUniversity / research
Drude–Sommerfeld Transport
Free-electron Drude model: scattering time τ, mobility μ, σ(ω), mean free path ℓ = v_Fτ, skin depth δ(ω), and DC Hall σ_xx(B), σ_xy(B).
- NewUniversity / research
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…
- NewUniversity / research
Landau Levels in a Magnetic Field
Charged particle in a uniform B-field: equally-spaced Landau ladder E_n = ℏω_c(n+½) with cyclotron frequency ω_c = qB/m, magnetic length…
- NewSchool
Maxwell–Boltzmann vs Eₐ
Translational energy density f(E); shaded fraction above activation energy; compare Arrhenius exp(−Eₐ/RT).
- NewSchool
Water P–T Phase Diagram
Qualitative fusion, sublimation, vapor pressure up to critical point — probe labeled regions (pedagogical curves).
- NewSchool
Binary Phase Diagram & Lever Rule
Isomorphous A–B T–x diagram: liquidus, solidus, tie line, and lever-rule phase fractions f_α and f_L for overall composition C₀.
- NewSchool
Diffusion Couple (Fick's Second Law)
Infinite A|B diffusion couple: error-function concentration profiles, diffusivity D, time t, and diffusion length 2√(Dt).
- NewSchool
Adsorption Isotherms
Langmuir, Freundlich, and BET isotherms: surface coverage, monolayer capacity n_m, and multilayer rise near P₀.
- NewSchool
Close Packing FCC / BCC / HCP
Coordination numbers, maximal packing η, schematic ABC vs AB stacking beside a BCC cubic cell.
- NewSchool
Chromatography Column
Partition chromatography cartoon: Gaussian bands separate as retention on the stationary phase differs.
- NewUniversity / research
Michaelis–Menten Kinetics
v vs [S] saturation and Lineweaver–Burk line from slope Km/Vmax and intercept 1/Vmax.
- NewSchool
DNA Replication (Schematic)
Fork, leading vs lagging strand, Okazaki fragments — static labeled cartoon.
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Polymer Random Coil
Lattice random walk R_g with Flory exponent ν slider (scaling hint vs Gaussian ν = ½).
- NewUniversity / research
Belousov–Zhabotinsky (Excitable)
Greenberg–Hastings excitable cellular automaton: target waves and rotating spirals as a qualitative BZ analogue.
- NewSchool
Radioactive Decay & Chain
N(t) from half-life T₁/₂; optional parent → daughter → stable Bateman ODEs (RK4, normalized).
- NewSchool
Le Châtelier Principle (Gas)
N₂ + 3H₂ ⇌ 2NH₃: T, V, add/remove species; Q vs K and relaxing mole bars.
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VSEPR Molecular Shapes (3D)
Bonding vs lone pairs on a central atom: AXₙEₘ notation, electron geometry, and ball–lone-pair model.
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Galvanic (Voltaic) Cell
Two half-cells, salt bridge, voltmeter; E°cell and Nernst E from ion concentrations (pedagogical E°).
- NewSchool
Hess's Law (Enthalpy Paths)
Two-step vs direct ΔH on an enthalpy diagram; sum must match declared overall ΔH.
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Collision Theory (2D Particles)
Hard-disk gas: elastic hits vs an activation speed threshold; T and Eₐ vs exp(−Eₐ/RT).
- NewSchool
Crystal Field Splitting (Oct / Tet)
Δ_t = (4/9)Δ_o; HS vs LS d⁴–d⁷ from CFSE + pairing P; toy complex hue vs Δ_oct.
- NewSchool
Unit Cell SC / BCC / FCC
Conventional cubic cells; yaw–pitch projection — lattice sites before basis detail.
- NewUniversity / research
Sequential Stern–Gerlach
Two SG devices: P(up on SG₂) = cos²(θ/2) or sin²(θ/2) after |±z⟩ filter.
- FeaturedKids
Molecule Viewer (3D)
Common molecules in 3D. Rotate, zoom. Ball-and-stick models.
- FeaturedKids
Periodic Table
Click element for properties, electron config, and uses.
- School
Electron Configuration
Fill orbitals visually with Aufbau principle animation.
- School
Balancing Equations
Interactive practice. Drag coefficients. Check balance.
- School
pH Scale
Slider from 0 to 14 with common substances and color indicators.
- School
Titration Simulator
Add base to acid. pH curve in real time. Find equivalence point.
- NewSchool
Reaction Rate
Arrhenius k(T), order 0/1/2, [A](t) curves and particle tank.
- NewSchool
Orbital Shapes (Schematic)
2D |ψ|² colormap for s-, p-, and d-like angular patterns (pedagogical, not HF).
- NewSchool
Particle in a 1D Box
Superposition of n=1 and n=2: time evolution of |Ψ|² and ⟨E⟩ (model units).
- NewUniversity / research
Gaussian Wave Packet
Free spreading: σ(t) from dispersion with ℏ = m = 1; uncertainty intuition.
- NewUniversity / research
Quantum Well Eigenstates (Box & HO)
Stationary ψ_n and |ψ_n|² for infinite square well or harmonic oscillator; optional phase animation (ℏ = 1).
- NewUniversity / research
Rectangular Barrier Tunneling
Analytic transmission T(E) vs energy for a 1D barrier; tunneling below V₀ and resonances above (ℏ = m = 1).
- NewSchool
Stern–Gerlach Beam (Cartoon)
Silver-like beam through an inhomogeneous B-field: atoms deflect to two detectors illustrating S_z = ±ℏ/2.
- NewUniversity / research
Bloch Sphere & Rabi Drive
Two-level Bloch vector with du/dt = u × ω, ω = (0, Ω, Δ); u_x–u_z view, Rabi flopping when Δ = 0.
- NewUniversity / research
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.
- NewSchool
Hydrogen: Balmer / Lyman Lines
Rydberg wavelengths 1/λ = R_H (1/n_f² − 1/n_i²); Lyman, Balmer, and Paschen series on a linear spectrum strip.
- NewUniversity / research
Heisenberg Product σ_x σ_p
Gaussian position and momentum widths with ℏ = 1; momentum “excess” over the minimum-uncertainty floor.
- NewUniversity / research
β⁻ Decay: Electron Spectrum
Continuous kinetic-energy spectrum up to endpoint Q (allowed-decay phase space); missing energy carried by the antineutrino.
- NewSchool
Nernst Equation
E = E° − (RT/nF) ln Q: sliders for E°, n, T, and reaction quotient.
- NewSchool
Buffer Solution
Henderson–Hasselbalch vs strong acid: pH curve as H⁺ is added (mole model).
- NewSchool
Acid Dissociation α(pH)
α = 1/(1+10^(pKa−pH)); half-equivalence at pH = pKa; curves for α and 1−α vs pH.
- NewSchool
Born–Haber Cycle (NaCl & CaO)
Step ΔH° table and enthalpy ladder; lattice energy U = Σ(gas-ion steps) − ΔH_f°.
- NewSchool
Frost Circle & Aromaticity (4n+2)
Inscribed n-gon on Hückel π energies; π count vs 4k+2 / 4k; Aufbau filling.
- NewSchool
Henry's Law (Gas Solubility)
p = k_H c with k_H(T) from ΔH; c vs T at fixed p (ideal-dilute sketch).
- NewUniversity / research
Gray–Scott Patterns
Reaction–diffusion u,v; coral / mitosis / worms / spirals; D_u, D_v, Δt.
- NewSchool
Gibbs Free Energy
ΔG = ΔH − TΔS; sign vs spontaneity at constant p,T (no Q or K).
- NewKids
Half-Life with Dice: Random Decay
Roll N dice, remove the ones that "decay"; N vs roll with theory N₀(1−p)ᵏ, T½ = ln 2/λ, log scale.