{
  "annotation_id": "3a9edb9a-0a53-404b-89ab-e040a67840b6",
  "date_created": "2026-03-02T18:02:40.985000Z",
  "date_modified": "2026-03-02T18:02:40.985000Z",
  "file_hash": "12391d81369f2946888a1ae7807a3271fa7ede2cc8a5eaf6c26e0d41aec07438",
  "private": false,
  "record": {
    "abstract": "We modify the Schr\\\"{o}dinger equation in a way that preserves its main\nproperties but makes use of higher order derivative terms. Although the\nmodification represents an analogy to the Doebner-Goldin modification, it can\ndiffer from it quite distinctively. A particular model of this modification\nincluding derivatives up to the fourth order is examined in greater detail. We\nobserve that a special variant of this model partially retains the linear\nsuperposition principle for the wave packets of standard quantum mechanics\nremain solutions to it. It is a peculiarity of this variant that a periodic\nstructure emerges naturally from its equations. As a result, a free particle,\nin addition to a plane wave solution, can possess band solutions. It is argued\nthat this can give rise to well-focused particle trajectories. Owing to this\npeculiarity, when interpreted outside quantum theory, the equations of this\nmodification could also be used to model pattern formation phenomena.",
    "arxiv_id": "quant-ph/9710007",
    "authors": [
      "Waldemar Puszkarz"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Higher Order Modification of the Schroedinger Equation",
    "url": "https://arxiv.org/abs/quant-ph/9710007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c8ce6380-1648-41dd-8b25-b4a7a92bb311",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}