Live 3D probability field
Renderer—
Input probability—
Vacuum gap—
Output probability—
Norm error—
Centroid x—
. input | material→vacuum − evanescent coupling vacuum→material | . output . numerical witness
input-side densitybounded vacuum regionoutput-side densitydrag field to rotate
Evidence boundary
Established: the nonrelativistic time-dependent Schrödinger equation, Born probability, FFT and unitary split-operator evolution.
Frozen model choices: the .|−|.. glyph, a closed periodic grid, a planar vacuum potential barrier, weak transverse confinement and the selected nondimensional baseline.
Not claimed: matter creation, particle transmutation, a laboratory vacuum, relativistic quantum-field interactions, measurement back-action or fabricated-device performance.
i ∂ψ/∂t = [−½∇² + V(x,y,z)] ψ
U(Δt) ≈ e−iVΔt/2 F−1 e−ik²Δt/2 F e−iVΔt/2
PL + Pvac + PR = ∑ |ψ|² = 1
Port and substrate specification
| Mark | Numerical object | Physical interpretation |
|---|---|---|
| . | normalized Gaussian packet | localized input matter state |
| | | | two planar interfaces at x = ±a | material boundaries enclosing the vacuum gap |
| − | sub-barrier wave amplitude | evanescent coupling through vacuum |
| . | PR | transformed output state |
| . | immutable snapshot | read-only numerical witness |
Numerical blueprint
| Grid | 32 × 16 × 16 complex samples |
| Spacing | Δx = Δy = Δz = 0.75 L₀ |
| Time step | Δt = 0.018 t₀ |
| Integrator | second-order Strang split operator |
| Kinetic step | separable radix-2 3D FFT |
| Boundary | periodic, closed computational volume |
| Example scale | L₀ = 1 nm, m* = mₑ → E₀ = —, t₀ = — |
Browser witness
Frozen verification
Contract: MST-3D-BC-1.0
Seal: b1924bad1f35783c…044b6d131ac4
Node conformance: 23/23 PASS
Stress: 1,000 split steps on 16×8×8