| _version_ | 1866902230802628608 |
|---|---|
| author | COPINET, Noel |
| author_facet | COPINET, Noel |
| contents | <div> <p>This demonstration builds upon and supersedes the Schrödinger derivation sketched in Fundamental theory of solitonic in dynamic 5D geometric space (HAL: hal-04987740v2).</p> <p>Here we provide a fully rigorous operator-level derivation (KLMN + spectral calculus), a compactification determined by an explicit one-loop effective potential, and a non-circular account of quantization. All original insights are preserved; proofs, operator domains, and error bounds are made explicit.</p> </div> <div>Reader's Roadmap (narrative) <p>We first describe, in plain words, how a deterministic five-dimensional geometry produces, at low energy, the time-dependent Schrödinger equation familiar to quantum mechanics. The route has three pillars. First, discreteness is an intrinsic outcome of topology and operator theory on S 1 /S 1 -Z N -no action constant required. Second, the physically realized sector (R, θ) is selected dynamically via an explicit one-loop effective potential. Third, the nonrelativistic dynamics emerges from a spectral expansion of √ A n with controlled remainders-no manual phase stripping. On this scaffold we place the full mathematics: closed forms and self-adjointness (KLMN), domain characterizations, spectral calculus for √ A n , Duhamel/Kato estimates, commutator bookkeeping, and time-dependent unitarity. Sections are written to balance intuition and rigor; the narrative ties the steps without blunting the precision of statements.</p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17350751 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | From 5D Solitonic Geometry to the Schrödinger Equation COPINET, Noel kaluza-klein casimir/hosotani schroedinger formula compactification spectral project 5D solitonic theory quantum mecanics <div> <p>This demonstration builds upon and supersedes the Schrödinger derivation sketched in Fundamental theory of solitonic in dynamic 5D geometric space (HAL: hal-04987740v2).</p> <p>Here we provide a fully rigorous operator-level derivation (KLMN + spectral calculus), a compactification determined by an explicit one-loop effective potential, and a non-circular account of quantization. All original insights are preserved; proofs, operator domains, and error bounds are made explicit.</p> </div> <div>Reader's Roadmap (narrative) <p>We first describe, in plain words, how a deterministic five-dimensional geometry produces, at low energy, the time-dependent Schrödinger equation familiar to quantum mechanics. The route has three pillars. First, discreteness is an intrinsic outcome of topology and operator theory on S 1 /S 1 -Z N -no action constant required. Second, the physically realized sector (R, θ) is selected dynamically via an explicit one-loop effective potential. Third, the nonrelativistic dynamics emerges from a spectral expansion of √ A n with controlled remainders-no manual phase stripping. On this scaffold we place the full mathematics: closed forms and self-adjointness (KLMN), domain characterizations, spectral calculus for √ A n , Duhamel/Kato estimates, commutator bookkeeping, and time-dependent unitarity. Sections are written to balance intuition and rigor; the narrative ties the steps without blunting the precision of statements.</p> </div> |
| title | From 5D Solitonic Geometry to the Schrödinger Equation |
| topic | kaluza-klein casimir/hosotani schroedinger formula compactification spectral project 5D solitonic theory quantum mecanics |
| url | https://doi.org/10.5281/zenodo.17350751 |