{"paper":{"title":"Generalized Unitarity and Reciprocity Relations for 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":"Ali Mostafazadeh","submitted_at":"2014-05-16T15:36:49Z","abstract_excerpt":"We derive certain identities satisfied by the left/right-reflection and transmission amplitudes, $R^{l/r}(k)$ and $T(k)$, of general ${\\cal PT}$-symmetric scattering potentials. We use these identities to give a general proof of the relations, $|T(-k)|=|T(k)|$ and $|R^r(-k)|=|R^l(k)|$, conjectured in [Z. Ahmed, J. Phys. A 45 (2012) 032004], establish the generalized unitarity relation: $R^{l/r}(k)R^{l/r}(-k)+|T(k)|^2=1$, and show that it is a common property of both real and complex ${\\cal PT}$-symmetric potentials. The same holds for $T(-k)=T(k)^*$ and $|R^r(-k)|=|R^l(k)|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4212","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"}