iℏ(∂ψ/∂t) = [H, ψ] + λ(x, t) / t^D(x) Hψ
where i is the imaginary unit, ℏ is the reduced Planck constant, ψ represents the wave function, H is the Hamiltonian operator, and λ(x, t) / t^D(x) accounts for fractal corrections.
Universal Scaling of Quantum State Transport:
We can show that the transport of a quantum state ψ(x) in the presence of potential V(x) exhibits universal scaling behavior. This means that the wave function ψ(x) evolves according to a scaling law:
ψ(x, t) ≈ ψ(x/t^α, t/t^(1-α))