{"paper":{"title":"Eigen Wavefunctions of a Charged Particle Moving in a Self-Linking Magnetic Field","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Dah-Wei Chiou, Dung-Hai Lee, Wu-Yi Hsiang","submitted_at":"2004-11-11T21:52:33Z","abstract_excerpt":"In this paper we solve the one-particle Schr\\\"{o}dinger equation in a magnetic field whose flux lines exhibit mutual linking. To make this problem analytically tractable, we consider a high-symmetry situation where the particle moves in a three-sphere $(S^3)$. The vector potential is obtained from the Berry connection of the two by two Hamiltonian $H(\\v{r})=\\hat{h}(\\v{r}) \\cdot\\vec{\\sigma}$, where $\\v{r}\\in S^3$, $\\hat{h}\\in S^2$ and $\\vec{\\sigma}$ are the Pauli matrices. In order to produce linking flux lines, the map $\\hat{h}:S^3\\to S^2$ is made to possess nontrivial homotopy. The problem is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0411044","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0411044/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}