{"paper":{"title":"Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"quant-ph","authors_text":"Dona Ghosh, Sachin Kumar, Zafar Ahmed","submitted_at":"2018-06-18T10:06:52Z","abstract_excerpt":"For complex PT-symmetric scattering potentials (CPTSSPs) $V(x)= V_1 f_{even}(x) + iV_2 f_{odd}(x), f_{even}(\\pm \\infty) = 0 = f_{odd}(\\pm \\infty), V_1,V_2 \\in \\Re $, we show that complex $k$-poles of transmission amplitude $t(k)$ or zeros of $1/t(k)$ of the type $\\pm k_1+ik_2, k_2\\ge 0$ are physical which yield three types of discrete energy eigenvalues of the potential. These discrete energies are real negative, complex conjugate pair(s) of eigenvalues (CCPEs: ${\\cal E}_n \\pm i \\gamma_n$) and real positive energy called spectral singularity (SS) at $E=E_*$ where the transmission and reflectio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06578","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"}