potentialSmearin
plain-language theorem explainer
The definition supplies the string label for the smearing of the Coulomb potential that arises when an electron samples the field over a finite region due to J-cost-driven position uncertainty. Atomic physicists modeling QED corrections to hydrogen levels would cite the label when tracing the 2S-2P splitting to vacuum fluctuations. The declaration is a direct string assignment with no computation or lemmas.
Claim. The smearing of the Coulomb potential is proportional to the expectation value of the squared radial displacement times the squared wave function at the origin: $⟨δr²⟩ |ψ(0)|²$.
background
Recognition Science models the Lamb shift as a modification of orbital J-cost caused by vacuum fluctuations. The electron jiggle is the position uncertainty induced by ledger J-cost variations, so the particle samples the Coulomb potential over a small region instead of at a single point. This sampling affects S-waves more strongly because their wave functions remain nonzero at r = 0, while P-waves are excluded from the origin by angular momentum.
proof idea
The declaration is a one-line wrapper that assigns the descriptive string for potential smearing.
why it matters
The label supports the module summary that lists five proven Lamb-shift claims, including the 1057.8 MHz numerical value and the leading α⁵ dependence. It names the concrete mechanism inside the RS derivation of the shift from J-cost fluctuations, linking the QFT-012 target to the upstream ledger factorization and phi-forcing structures that calibrate J.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.