{"paper":{"title":"Minimal Position-Velocity Uncertainty Wave Packets in Relativistic and Non-relativistic Quantum Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"M. H. Al-Hashimi, U.-J. Wiese","submitted_at":"2009-07-29T19:40:46Z","abstract_excerpt":"We consider wave packets of free particles with a general energy-momentum dispersion relation $E(p)$. The spreading of the wave packet is determined by the velocity $v = \\p_p E$. The position-velocity uncertainty relation $\\Delta x \\Delta v \\geq {1/2} |< \\p_p^2 E >|$ is saturated by minimal uncertainty wave packets $\\Phi(p) = A \\exp(- \\alpha E(p) + \\beta p)$. In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation $E(p) = p^2/2m$, analytic calculations are presented for the spreading of wave packets with minimal position-velocity unce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5178","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"}