IndisputableMonolith.Physics.SchroedingerEquationFromRS
Module framing quantum mechanics inside Recognition Science: a QM system is a finite set of recognition modes, stationary states are those with vanishing J-cost (recognition equilibrium), and superpositions are convex combinations of modes. It packages a certificate that the stationary condition recovers the time-independent Schrödinger picture. Physicists linking RS cost geometry to eigenstates would cite it. Mostly definitional scaffolding over the Cost import.
claimA quantum system is a finite collection of recognition modes. A state is stationary when its J-cost vanishes ($J=0$), identified with an eigenstate (recognition equilibrium). Superpositions are convex combinations of modes. A Schrödinger certificate asserts that this stationary condition matches the time-independent Schrödinger eigenvalue picture in RS units.
background
Recognition Science treats physical cost via the unique J-functional forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), from the T5 step of the forcing chain. The Cost module supplies that $J$ and its elementary identities.
This physics module lifts that cost into a discrete quantum setting. A QM system is a finite mode set; the count of modes is recorded explicitly. Stationary states are defined by the equilibrium condition $J=0$, read as eigenstates of the recognition dynamics. Superposition is the convex combination of such modes, keeping the construction inside the RS cost geometry rather than Hilbert-space axioms from scratch.
The local goal is to certify that the RS stationary condition reproduces the time-independent Schrödinger picture (energy eigenstates as cost minima), not yet the full time-dependent unitary flow.
proof idea
This is primarily a definition module. It introduces the QM-system carrier, the mode count, the stationary-state predicate ($J=0$), superposition as a combination of modes, and a Schrödinger certificate structure together with a default instance. There is no deep tactic proof body at module scope; the argument is the identification of vanishing J-cost with recognition equilibrium, imported from Cost, packaged so downstream physics lemmas can assume a certified QM system.
why it matters in Recognition Science
Places the Schrödinger stationary picture on the same J-cost footing as the rest of Recognition Science, so mass-ladder and coupling results can treat eigenstates as $J=0$ equilibria rather than as an external quantum postulate. Feeds any later derivation that needs a certified link from RS cost to the time-independent Schrödinger equation. No downstream consumers are wired in the graph yet; the module is an entry point for the physics layer above Cost and the forcing chain (T5 J-uniqueness). It does not yet close the time-dependent or measurement sides of QM.
scope and limits
- Does not derive the time-dependent Schrödinger equation or unitary evolution.
- Does not construct Hilbert space, operators, or spectra from first principles.
- Does not prove uniqueness of the stationary-state identification beyond J=0.
- Does not connect to the mass ladder, alpha band, or eight-tick octave.
- Does not supply numerical predictions or experimental bounds.