{"paper":{"title":"Schr\\\"odinger formalism for a particle constrained to a surface in $\\mathbb{R}_1^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Eduardo S. G. Leandro, Fernando Moraes, Luiz C. B. da Silva, Renato Teixeira","submitted_at":"2018-05-18T20:17:15Z","abstract_excerpt":"In this work it is studied the Schr\\\"odinger equation for a non-relativistic particle restricted to move on a surface $S$ in a three-dimensional Minkowskian medium $\\mathbb{R}_1^3$, i.e., the space $\\mathbb{R}^3$ equipped with the metric $\\text{diag}(-1,1,1)$. After establishing the consistency of the interpretative postulates for the new Schr\\\"odinger equation, namely the conservation of probability and the hermiticity of the new Hamiltonian built out of the Laplacian in $\\mathbb{R}_1^3$, we investigate the confining potential formalism in the new effective geometry. Like in the well-known Eu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07428","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}