{"paper":{"title":"Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"B. Mojaveri, H. Fakhri, M.A. Gomshi Nobary","submitted_at":"2014-04-15T07:35:54Z","abstract_excerpt":"We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\\vec{B}=-B_{0}e^{-\\frac{2\\pi}{a_{0}}x}\\hat{k}$ with $B_{0}>0$ as a constant strength and $a_{0}$ as the width of the band. It is shown that the square integrable pure states realize representations of $su(1,1)$ algebra via the quantum number corresponding to the linear momentum in the $y$-direction. The energy of the states increases by decreasing the width $a_{0}$ while it is not changed by $B_{0}$. It is quadratic in terms of two quan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3837","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":""},"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"}