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.