Maximum Quantum Numbers and Hydrogen Chemistry from The Prince Equation

We derive fundamental limits on quantum numbers for hydrogen from geometric constraints in The Prince Equation (de Broglie’s relation interpreted as spacetime curvature). The requirement that bound states satisfy 0 < θ < π/2 with angularquantization δθ = 1/(2π) yields a maximum quantum number nmax = π2−1 ≈ 8.87. This explains the observed cutoff in hydrogen spectral lines, the origin of hydrogen’s chemical reactivity, and provides physical meaning to wave-particle duality anduncertainty principles as boundary phenomena. No infinite ladder of states exists contrary to standard quantum mechanics.