{
  "annotation_id": "19187185-dafb-47dd-a076-31e7f3e51753",
  "date_created": "2026-03-02T18:02:27.442000Z",
  "date_modified": "2026-03-02T18:02:27.442000Z",
  "file_hash": "6eb80d4052ecc9cb03d8b6a2306187268dc9d9f7a61c728eb021af0a756374c4",
  "private": false,
  "record": {
    "abstract": "An differential equation for wave functions is proposed, which is equivalent\nto Schr\\\"{o}dinger\u0027s wave equation and can be used to determine energy-level\ngaps of quantum systems. Contrary to Schr\\\"{o}dinger\u0027s wave equation, this\nequation is on `bipartite\u0027 wave functions. It is shown that those `bipartite\u0027\nwave functions satisfy all the basic properties of Schr\\\"{o}dinger\u0027s wave\nfunctions. Further, it is argued that `bipartite\u0027 wave functions can present a\nmathematical expression of wave-particle duality. This provides an alternative\napproach to the mathematical formalism of quantum mechanics.",
    "arxiv_id": "quant-ph/0604083",
    "authors": [
      "Zeqian Chen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Wave equations for determining energy-level gaps of quantum systems",
    "url": "https://arxiv.org/abs/quant-ph/0604083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2cbb4fc3-5b70-45b5-a471-dfd66570a8ea",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}