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.