{"paper":{"title":"From interpretation of the three classical mechanics actions to the wave function in quantum mechanics","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["physics.class-ph","physics.hist-ph"],"primary_cat":"quant-ph","authors_text":"Alexandre Gondran, Michel Gondran","submitted_at":"2012-10-10T15:37:56Z","abstract_excerpt":"First, we show that there exists in classical mechanics three actions corresponding to different boundary conditions: two well-known actions, the Euler-Lagrange classical action S_cl(x,t;x_0), which links the initial position x_0 and its position x at time t, the Hamilton-Jacobi action S(x,t), which links a family of particles of initial action S_0(x) to their various positions x at time t, and a new action, the deterministic action S(x,t;x_0,v_0), which links a particle in initial position x_0 and initial velocity v_0 to its position x at time t. We study, in the semi-classical approximation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3025","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"}