Modification of the Schr¨odinger Equation in Twistor-EBIKK-β Gravity

We derive the modified Schr¨odinger equation within the framework of Twistor-Entropic-BornInfeld-Kaluza-Klein gravity with β-regularization (Twistor-EBIKK-β). The equation incorporatesthree fundamental modifications: (1) a twistor-induced UV regularization term κ|Z|2, (2) an entropicgravity contribution Tent ln(det G), and (3) a spin-twistor coupling κℏ4m σ ·(∇ × AZ ) for fermions. Weshow that the standard Schr¨odinger equation emerges in the limit κ, Tent, β → 0, while new testableeffects appear when these parameters take their predicted values (κ1/4 ∼ 10 TeV, Tent ∼ 0.1 − 1eV). The model predicts measurable corrections to atomic spectra, g-factors, and quantum tunnelingprobabilities.