TauTimp · Electron Equation

TauTimp Orbital Atlas

Every hydrogenic orbital — s, p, d, f — with an identical spatial shape (Taylor-verified, §4), but two different time dynamics: the stationary Schrödinger state vs. the pulsating unduscular wave.

Family

Shell (n)

Orientation

Dynamic model

1.0×

Current state

Orbital

n, l

1, 0

Energy E_n

−13.6057 eV

Sample radius

7 a₀

Points |ψ|²

–

Model

Schrödinger

positive lobe / shell

negative lobe / shell

Radial part R_nl(r) computed generally via associated Laguerre polynomials (∝ e^−r/nρ^lL_n−l−1^2l+1(ρ), ρ=2r/n); angular part from the real Cartesian solid harmonics (s,p,d,f). Cloud sampled by Monte Carlo from |ψ|²; the fine shells in unduscular mode represent — exaggerated, for visibility — the periodic zero structure at the Compton scale (§12). Derived from electron_TauTimp_final_RO.md, §4 and §11–12 (Popescu, 2026).

sampling the probability cloud…

drag to rotate · scroll to zoom