More from Chemistry
Other simulators in this category — or see all 48.
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. The 1σ ellipse rotates by half the squeeze phase θ/2 and shrinks below the vacuum floor along one quadrature — the basic picture of CV quantum optics.
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).
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 spirals inside the sphere — the geometric picture of decoherence with live populations P(|0⟩), purity Tr ρ², and time traces of u_x, u_y, u_z.
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}) — fringe period 2π/Δ, exponential T₂ envelope; the Bloch sphere animates each stage. Foundational to atomic clocks and Ramsey interferometry.
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√2 ≈ 2.828 at the canonical Bell angles (0°, 90°, 45°, −45°), violating the local-realist limit |S| ≤ 2 — quantum entanglement made statistically visible.