{"paper":{"title":"On the Number of Bound States of Point Interactions on Hyperbolic Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fatih Erman","submitted_at":"2015-11-24T12:15:30Z","abstract_excerpt":"We consider the problem of a quantum particle interacting with $N$ attractive point $\\delta$-interactions in two and three dimensional Riemannian manifolds and discuss its some spectral properties. The main aim of this paper is to give a sufficient condition for the Hamiltonian to have $N$ bound states and give an explicit criterion for it in hyperbolic manifolds $\\mathbb{H}^2$ and $\\mathbb{H}^3$. Furthermore, we study the same spectral problem for a relativistic extension of the model on $\\mathbb{R}^2$ and $\\mathbb{H}^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07670","kind":"arxiv","version":4},"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"}