Proof that the Electron is a Closed Surface of Bohr Radius

This paper presents a formal proof that the electron is not a point particle but a closed surface structure with a radius equal to the Bohr radius. By analyzing the Laplacian of the hydrogen atom’s ground-state wavefunction, we show that the curvature density of the spatial distribution, given by ∇2Φ/Φ, attains a finite and well-defined value of approximately -1 / a₀², where a₀ is the Bohr radius. This finite curvature contradicts the point-particle assumption and supports the interpretation of the electron as a quantized closed surface. The result offers a geometric foundation for reinterpreting quantum entities in terms of surface-based, not point-based, structures.