Schrödinger Wave Mechanics: Complete Mathematical Atlas and USP-Compatible Resonance Commentary

How much of Schrödinger’s mathematical work can inform a modern resonance-geometry interpretation without rewriting the history of quantum mechanics? msf:53020 v2.0.1 is a historical and mathematical atlas spanning the structures most relevant to stationary quantum states and future USP development. The document separates four layers throughout: historical source mathematics, modern normalized formulation, USP-compatible interpretation, and explicit limits on what the mathematics establishes. The atlas covers eigenvalue quantization, wave/matrix equivalence, variational methods, hydrogen, the harmonic oscillator, perturbation theory, wave packets, probability current and continuity, uncertainty covariance, energy exchange, Dirac slow/fast motion, curved-spacetime spinors, endpoint-conditioned diffusion, global phase, expanding-geometry modes, factorization, entanglement, quantum jumps, and measurement. The stationary-state architecture remains standard quantum mechanics: Ĥψₙ = Eₙψₙ, Ψₙ(r,t) = ψₙ(r)e^(−iEₙt/ℏ). USP-compatible resonance language is introduced only as an interpretation of already-defined quantum structures. It does not replace the Hamiltonian, Born statistics, spinor structure, phase/current information, or detector theory. Historical compatibility is not evidence for a USP substrate or new dynamics. No nonzero USP residual is claimed: A_USP = 0. *SHORT ZENODO SUMMARY A historical-mathematical atlas of Schrödinger wave mechanics spanning eigenvalue quantization, uncertainty covariance, wave packets, relativistic and curved-space structures, factorization, entanglement, and measurement. USP-compatible resonance language is kept strictly interpretive, with standard quantum mechanics as the predictive baseline and A_USP = 0 as the exact null.