Fine Structure Constant Derivation from de Broglie Vector Equation.

We derive the fine structure constant directly from the de Broglie vector equation in its dot product form for bound states. The simplicity of this derivation emerges from recognizing that bound states require both cross product (tangential) and dot product (radial) components when the binding angle θ < 90◦. The fine structure constant emerges as α = (v(t)/c) cos θ where v(t) is the tangential velocity.