{
  "annotation_id": "a51f2479-9050-4cf7-b5f6-bfdce5fb31b3",
  "date_created": "2026-03-02T18:01:18.146000Z",
  "date_modified": "2026-03-02T18:01:18.146000Z",
  "file_hash": "f61534611e81e74712bd4867c99ead37970ae4cf15ea124c395873f094b6067b",
  "private": false,
  "record": {
    "abstract": "We have developed a new family of limited-diffraction electromagnetic\nX-shaped waves based on the scalar \"X waves\" discovered previously. These waves\nare diffraction-free in theory and particle-like (wave packets), in that they\nmaintain their shape as they propagate to an infinite distance. The X waves\npossess (theoretically) infinitely extended arms, and --at least, the ones\nstudied in this paper-- have an infinite total energy: therefore, they are not\nphysically realizable. However, they can be truncated in both space and time\nand approximated by means of a finite aperture radiator so to get a large\nenough depth of interest (depth of field). In addition to the Maxwell\nequations, X wave solutions to the free Schroedinger equation are also\nobtained. Possible applications of these new waves are discussed. Finally, we\ndiscuss the appearance of the X-shaped solutions from the purely geometric\npoint of view of the Special Relativity theory. [PACS nos. 03.40.Kf, 03.50.De,\n41.20.Jb, 41.20.Bt, 42.25.Bs, 03.30.+p, 03.65.-w].",
    "arxiv_id": "physics/9610012",
    "authors": [
      "Jian-yu Lu",
      "J. F. Greenleaf",
      "Erasmo Recami"
    ],
    "categories": [
      "physics.gen-ph",
      "physics.class-ph",
      "quant-ph"
    ],
    "title": "Limited-Diffraction Solutions to Maxwell and to Schroedinger Equations",
    "url": "https://arxiv.org/abs/physics/9610012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f5a89a7d-1a1b-4cf1-ae7f-5a0254601ba5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}