{
  "id": "quant-ph/0306013",
  "version": "v1",
  "published": "2003-06-02T13:31:42.000Z",
  "updated": "2003-06-02T13:31:42.000Z",
  "title": "Shapes of Quantum States",
  "authors": [
    "Dorje C. Brody"
  ],
  "comment": "Submitted to Proc. R. Statist. Soc",
  "journal": "Journal of Physics A37, 251-257 (2004)",
  "doi": "10.1088/0305-4470/37/1/017",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of points. Various correspondences between point configurations and quantum states, such as linear superposition as well as unitary and stochastic evolution of shapes, are illustrated. In particular, a complete characterisation of shape eigenstates for an arbitrary number of points is given in terms of cyclotomic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-02T13:31:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pure quantum states",
      "point configurations",
      "quantum mechanics",
      "planar configurations",
      "shape space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2004,
      "month": "Jan",
      "volume": 37,
      "number": 1,
      "pages": 251
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004JPhA...37..251B"
    }
  }
}