LFM-PAPER-051: Hydrogen Molecule from Single-Equation LFM

This paper demonstrates that molecular bound states emerge from the Lattice Field Medium (LFM) equation framework established in Paper 50. We simulate the hydrogen molecular ion (H₂⁺) as a single electron in overlapping Coulomb χ-wells representing two protons. Using imaginary time evolution to find the ground state at each bond length, we construct the binding curve and verify molecular formation. Key results: Stable H₂⁺ bound state forms with binding energy 3.42 eV (vs 2.8 eV in 3D—good agreement) Equilibrium bond length is 7.21 Bohr radii (longer than 3D due to 2D simulation dimensionality) Electron density shows classic bonding orbital character with electron shared between protons Clear binding curve showing repulsion at short range, binding at intermediate range The core finding: Chemistry emerges from LFM wave dynamics. The same equation that produces gravity and dark matter (Paper 50) also produces molecular bonds. Coulomb potentials in LFM are simply χ-wells, and molecular orbitals emerge as stable wave patterns in the E field. This paper is part of the LFM Foundational Papers series demonstrating that a single wave equation unifies physics from galaxies to atoms.