{
  "annotation_id": "01999485-195a-439f-b863-c35dd9f70753",
  "date_created": "2026-03-02T18:02:34.731000Z",
  "date_modified": "2026-03-02T18:02:34.731000Z",
  "file_hash": "d51a6c83268ed9f77f8a8fb4e19128f382bcd8074e176659d1af81a6f514a6a1",
  "private": false,
  "record": {
    "abstract": "The aim of Part II of this paper is to try to describe wave functions on\nq-deformed versions of position and momentum space. This task is done within\nthe framework developed in Part I of the paper. In order to make Part II\nself-contained the most important results of Part I are reviewed. Then it is\nshown that q-deformed exponentials and q-deformed delta functions play the role\nof momentum and position eigenfunctions, respectively. Their completeness and\northonormality relations are derived. For both bases of eigenfunctions matrix\nelements of position and momentum operators are calculated. A q-deformed\nversion of the spectral decomposition of multiplication operators is discussed\nand q-analogs of Heaviside functions are proposed. Interpreting the results\nfrom the point of view provided by the concept of quasipoints gives the\nformalism a physical meaning. The definition of expectation values and the\ncalculation of probability densities are explained in detail. Finally, it is\noutlined how the considerations so far carry over to antisymmetrized spaces.",
    "arxiv_id": "quant-ph/0612174",
    "authors": [
      "Hartmut Wachter"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum kinematics on q-deformed quantum spaces II, Wave functions on   position and momentum space",
    "url": "https://arxiv.org/abs/quant-ph/0612174"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "936bf4d3-965e-42c0-86a6-8ee351f4ab24",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}