SOVEREIGN · LIVE EQUATION MAP

Anatomy of the Schrödinger Equation

Every colored symbol is wired to the scene. Hover a term to see what it owns out there; click to pin it; move a slider and the term it belongs to flashes.

THE TIME-DEPENDENT SCHRÖDINGER EQUATION — HOVER ANY COLORED TERM

THE EXACT WAVE PACKET BEING DRAWN (UNITS ℏ = 1)

k · wavenumber — momentum, coil tightness

m · mass — heavier turns slower (ω = ℏk²/2m)

σ · packet width — where the particle might be

∂/∂t · playback of time evolution

V(x) · potential barrier height V₀

i · what if the imaginary unit weren’t there?

|Ψ|² · Born rule — probability density curtain

ω = ℏk²/2m

E = ℏω

v𝜑 = ω/k

TUNNEL T

Ψ(x,t) lives in the complex plane: height = Re Ψ, depth = Im Ψ. The corkscrew is not decoration — it is what “complex-valued” looks like.

Ψ wavefunction (cyan helix)
Re Ψ vertical axis
Im Ψ depth axis — the work of i
x position axis
V(x) potential wall
|Ψ|² probability curtain (back wall)

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