{
  "annotation_id": "b0194ae6-759d-4ccb-84de-167f401d5ecd",
  "date_created": "2026-03-02T18:02:48.351000Z",
  "date_modified": "2026-03-02T18:02:48.351000Z",
  "file_hash": "3b86a98e13539d052a8a9a9de19949180295672c073180b1d9ce893f124883a3",
  "private": false,
  "record": {
    "abstract": "The interpretation of quantum mechanics due to Lande\u0027 is applied to the\nconnection between wave mechanics and matrix mechanics. The connection between\nthe differential eigenvalue equation and the matrix eigenvalue equation for an\noperator is elucidated. In particular, we show that the elements of a matrix\nvector state are probability amplitudes with a structure rather than being mere\nconstants. We obtain the most general expressions for the probability\namplitudes for the description of spin-1/2 measurements. As a result, we derive\nspin-1/2 operators and vectors from first principles. The procedure used is\nanalogous to that by which orbital angular momentum wavefunctions and operators\nare transformed to matrix mechanics vectors and matrices. The most generalized\nforms of the spin operators and their eigenvectors for spin-1/2 are derived and\nshown to reduce to the Pauli spin matrices and vectors in an appropriate limit.",
    "arxiv_id": "quant-ph/9905012",
    "authors": [
      "Habatwa Vincent Mweene"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Derivation of Spin Vectors and Operators From First Principles",
    "url": "https://arxiv.org/abs/quant-ph/9905012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3339f12c-139c-46c7-9ae0-d896e42ad541",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}