The Schrödinger Equation from the Shift

The Schrödinger equation is derived from the shift map on the Tree of Continua 1. Nopostulates. No quantization procedure. No correspondence principle. The shift σ(x)(i) =x(i + 1) is the unique canonical dynamical map on the Tree of Continua. It is uniformlycontinuous in the Weil uniform structure 3 on the tree. Its IPG reading at ∞ is a stronglycontinuous one-parameter unitary group. Stone’s theorem 5 gives a self-adjoint generatorH. The Schrödinger equation iħψ̇ = Hψ is the infinitesimal form of the shift at the IPGreading at ∞. ħ is the grade step expressed in continuous units — a conversion factor, nota constant of nature.