Quantum Extension: Modified Schrödinger Equation in Fractal Spacetime via Ibaguner Constant 0.3715 and Ibaguner Fractal Operator IFO

Interpretation as Fractal Metric DeformationUnlike classical fractional quantum mechanics based on L´evy processes, the present formulation arises from entropy scaling and fractal geometry.Thus:• it does not assume stochastic jumps,• it encodes deterministic fractal structure,• it generalizes the notion of spatial derivatives. Testable Predictions• Modified dispersion in cold atom systems• Anomalous diffusion signatures• Suppressed wave packet spreading• Non-Gaussian interference patternsInterpretation as Fundamental EquationWe propose that the above equation represents a candidate “fundamental equation of existence,” in which:• exponential decay (Euler structure),• fractal geometry,• and quantum evolutionare unified within a single dynamical law.