{"paper":{"title":"Integral formulation of the quantum mechanics in the phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Tomas Zimmermann","submitted_at":"2018-06-14T06:29:50Z","abstract_excerpt":"A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\\text{\\reflectbox{\\text{p}}}\\mkern-3mu\\text{p}\\left(q,p\\right)$ which might be computed from the position-space wave function $\\psi\\left(q\\right)$ with a transformation related to the Gabor transformation. The equation of motion for conservative systems can be written in the form of the Schr\\\"{o}dinger equation with a $4D$-dimensional Hamiltonian with classical terms on the diagonal and complex off-diagonal couplings. The Hamiltonian does not contain any differential operators and the quanti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05383","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"}