{
  "id": "2304.03176",
  "version": "v1",
  "published": "2023-04-02T12:41:34.000Z",
  "updated": "2023-04-02T12:41:34.000Z",
  "title": "Quantum mechanics on a circle with a finite number of α-uniformly distributed points",
  "authors": [
    "Won Sang Chung",
    "Ilyas Haouam",
    "Hassan Hassanabadi"
  ],
  "comment": "9 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In this paper, quantum mechanics on a circle with finite number of {\\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete angular momentum operators and Hermitian Hamiltonian on a circle with d {\\alpha}-distributed discrete angles are constructed. The energy levels are computed for a free particle on a circle where the wave function is defined in the d {\\alpha}-distributed discrete angles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-02T12:41:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite number",
      "quantum mechanics",
      "distributed points",
      "discrete angular momentum operators",
      "discrete angle representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}