Closed Surface Series #2: The Hydrogen Atom as a Dual Closed Surface System

This paper proposes a new structural interpretation of the hydrogen atom as a dual closed surface system. The central proton is modeled as a minimal closed surface, while the electron forms a quantized spherical closed surface with radius approximately equal to the Bohr radius. The spatial curvature derived from the Laplacian of the wavefunction supports this shell-like structure. Quantum transitions between energy levels are reinterpreted as topological mode reconstructions of the electron’s surface, rather than point transitions. This framework provides a consistent geometric basis for understanding atomic structure and the origin of quantum numbers.