{
  "annotation_id": "f83b00c1-fb69-498a-93ba-6a82d1ced29c",
  "date_created": "2026-03-02T18:02:13.804000Z",
  "date_modified": "2026-03-02T18:02:13.804000Z",
  "file_hash": "3ab2bea19d687a16455b5b5dba8fa5183516bd66b8df75465901f9e2aba11dfe",
  "private": false,
  "record": {
    "abstract": "A powerful method for calculating the eigenvalues of a Hamiltonian operator\nconsists of converting the energy eigenvalue equation into a matrix equation by\nmeans of an appropriate basis set of functions. The convergence of the method\ncan be greatly improved by means of a variational parameter in the basis\nfunctions determined by the principle of minimal sensitivity. In the case of\nthe quartic anharmonic oscillator and of a symmetrical double-well potential we\nchoose an effective oscillator frequency. In the case of nonsymmetrical\npotential we add a coordinate shift in a two-parameter variational calculation.\nThe method not only gives the spectrum, but also an approximation to the energy\neigenfunctions. Consequently it can be used to solve the time-dependent\nSchr\\\"odinger equation using the method of stationary states. We apply it to\nthe time development of two different initial wave functions in the double-well\nslow roll potential.",
    "arxiv_id": "quant-ph/0412082",
    "authors": [
      "Paolo Amore",
      "Alfredo Aranda",
      "Francisco Fernandez",
      "Hugh Jones"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "A non-perturbative method for time-dependent problems in quantum   mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0412082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eb5f285d-f915-4b82-8a0d-d0ef5e97c070",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}