{
  "annotation_id": "8a158832-f53d-4fb8-b9d5-d50d027a7ea5",
  "date_created": "2026-03-02T18:01:14.816000Z",
  "date_modified": "2026-03-02T18:01:14.816000Z",
  "file_hash": "883ef7b53d4556e8c0fc5d6a41b3aac38c40c128314c1093d8587d28b6829461",
  "private": false,
  "record": {
    "abstract": "This is the second installment of a two-part paper on developments in quantum\ndispersion theory leading up to Heisenberg\u0027s \"Umdeutung\" paper. In telling this\nstory, we have taken a paper by John H. Van Vleck as our main guide. In this\nsecond part we present the detailed derivations on which our narrative in the\nfirst part rests. The central result that we shall derive is the Kramers\ndispersion formula, which played a key role in the thinking that led to\nHeisenberg\u0027s \"Umdeutung\" paper. Closely following Van Vleck\u0027s pre-Umdeutung\napproach, we derive classical and construct quantum formulae for the\ndispersion, emission, and absorption of radiation both for the special case of\na charged harmonic oscillator (sec. 5) and for arbitrary non-degenerate\nmultiply-periodic systems (sec. 6). In sec. 7, we rederive the same results\nusing modern quantum mechanics. In sec. 8 we bring together the main\nconclusions of our study.",
    "arxiv_id": "physics/0610193",
    "authors": [
      "Anthony Duncan",
      "Michel Janssen"
    ],
    "categories": [
      "physics.hist-ph"
    ],
    "title": "On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence   principle (Part Two)",
    "url": "https://arxiv.org/abs/physics/0610193"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1e83ced0-68af-40ed-a35d-f87d92eb39d3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}