{"paper":{"title":"Symmetric Fermi-type potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Sachin Kumar, Sarthak Hajirnis, Tarit Goswami, Zafar Ahmed","submitted_at":"2019-04-03T12:20:46Z","abstract_excerpt":"We utilize the amenability of the Fermi-type potential profile in Schr{\\\"o}dinger equation to construct a symmetric one dimensional well as $V(x){=}{-}U_n/[1+\\exp[(|x|{-}a)/b]], ~ U_n{=}V_n[1+\\exp[-a/b]]$. We define $\\alpha=a/b, ~\\beta_n {=}b\\sqrt{2m U_n}/\\hbar$, we find $\\beta_n$ values for which critically the well has $n$-node half bound state at $E{=}0$. Consequently, this fixed well has $n$ number of bound states. Also we obtain a semi-classical expression ${\\cal G}(\\alpha,\\beta)$ such that the Fermi well has either $[\\cal G]$ or $[{\\cal G}]+1$ number of bound states. Here $[.]$ indicates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02284","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"}