{
  "annotation_id": "4c0f4c0e-66e8-4825-a04b-9deb9072dc4c",
  "date_created": "2026-03-02T18:02:37.251000Z",
  "date_modified": "2026-03-02T18:02:37.251000Z",
  "file_hash": "0861275129b94a62699f1404aeffe4333e2839402115df385ffcbc9923d94e8d",
  "private": false,
  "record": {
    "abstract": "It is shown that von Neumann-Landau equation for wave functions can present a\nmathematical formalism of motion of quantum mechanics. The wave functions of\nvon Neumann-Landau equation for a single particle are `bipartite\u0027, in which the\nassociated Schr\\\"{o}dinger\u0027s wave functions correspond to those `bipartite\u0027\nwave functions of product forms. This formalism establishes a mathematical\nexpression of wave-particle duality and that von Neumann\u0027s entropy is a\nquantitative measure of complementarity between wave-like and particle-like\nbehaviors. Furthermore, this extension of Schr\\\"{o}dinger\u0027s form suggests that\ncollapses of Schr\\\"{o}dinger\u0027s wave functions can be regarded as the\nsimultaneous transition of the particle from many levels to one.",
    "arxiv_id": "quant-ph/0703204",
    "authors": [
      "Zeqian Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "von Neumann-Landau equation for wave functions, wave-particle duality   and collapses of wave functions",
    "url": "https://arxiv.org/abs/quant-ph/0703204"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d5d2823a-11db-48c3-84ed-69e3e6950e53",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}