{"paper":{"title":"Peculiarities of squaring method applied to construct solutions of the Dirac, Majorana, and Weyl equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"O.V. Veko, V.M. Red'kov","submitted_at":"2015-01-25T15:55:14Z","abstract_excerpt":"It is shown that the known method to solve the Dirac equation by means of the squaring method, when relying on the scalar function of the form \\Phi = e^{-i\\epsilon t} e^{ik_{1} x} e^{ik_{2} y} \\sin (kz + \\alpha) leads to a 4-dimensional space of the Dirac solutions. It is shown that so constructed basis is equivalent to the space of the Dirac states relied on the use of quantum numbers k_{1}, k_{2}, \\pm k and helicity operator; linear transformations relating these two spaces are found. Application of the squaring method substantially depends on the choice of representation for the Dirac matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06175","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"}