The Zulfia Quantum Ziwave Equation: Schr¨odinger as a Special Case

For more than a century since Schr¨odinger, the quantum wave equation has been as-sumed to hold on a fully accessible domain Ω without certified origin. No extension in theavailable literature has revisited its foundational probability assumption.We replace this assumption with a deviation origin. Using Zulfia Decomposition inProbability (ZDM) Z(t) = MZ [η(t0)] + ∆(t) within Zulfia Bi-Face Probability Theory(ZBPT) [1], the information field after collision is restricted to deviation domain Ω \ ΩC =∆−1(̸= 0) where ∆(t)̸ = 0 where PZ does not exist and C(ω) = 0, with certified domainΩC = ∆−1(0) excluded where ∆(t) = 0.iℏZ CZ (ω) ∂∆(t)∂t = − ℏ2Z2mZ∇ · (CZ (ω)∇∆(t)) + VZ (ω)∆(t) on Ω \ ΩC (1)The conventional equationiℏ∂tψ = − ℏ22m ∇2ψ + V ψ (2)is the special case for Ω \ ΩC ≈ Ω, CZ = 1.After Collision is strictly informational, mass-free on Ω \ ΩC .