{"paper":{"title":"Solutions of a particle with fractional $\\delta$-potential in a fractional dimensional space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Sami I. Muslih","submitted_at":"2010-01-25T20:58:27Z","abstract_excerpt":"A Fourier transformation in a fractional dimensional space of order $\\la$ ($0<\\la\\leq 1$) is defined to solve the Schr\\\"odinger equation with Riesz fractional derivatives of order $\\a$. This new method is applied for a particle in a fractional $\\delta$-potential well defined by $V(x) =- \\gamma\\delta^{\\la}(x)$, where $\\gamma>0$ and $\\delta^{\\la}(x)$ is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if $0< \\la<\\a$. The results for $\\la= 1$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4352","kind":"arxiv","version":2},"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"}