{
  "id": "2111.01546",
  "version": "v2",
  "published": "2021-10-30T20:16:27.000Z",
  "updated": "2021-12-30T22:04:45.000Z",
  "title": "From quartic anharmonic oscillator to double well potential",
  "authors": [
    "Alexander V. Turbiner",
    "J. C. del Valle"
  ],
  "comment": "7 pages, extended, two figures added, to be published at Acta Polytechnica",
  "journal": "Acta Polytechnica 62(1): 208-210, 2022",
  "doi": "10.14311/AP.2022.62.0208",
  "categories": [
    "quant-ph",
    "physics.atom-ph"
  ],
  "abstract": "It is already known that the quantum quartic single-well anharmonic oscillator $V_{ao}(x)=x^2+g^2 x^4$ and double-well anharmonic oscillator $V_{dw}(x)= x^2(1 - gx)^2$ are essentially one-parametric, their eigenstates depend on a combination $(g^2 \\hbar)$. Hence, these problems are reduced to study the potentials $V_{ao}=u^2+u^4$ and $V_{dw}=u^2(1-u)^2$, respectively. It is shown that by taking uniformly-accurate approximation for anharmonic oscillator eigenfunction $\\Psi_{ao}(u)$, obtained recently, see JPA 54 (2021) 295204 [1] and Arxiv 2102.04623 [2], and then forming the function $\\Psi_{dw}(u)=\\Psi_{ao}(u) \\pm \\Psi_{ao}(u-1)$ allows to get the highly accurate approximation for both the eigenfunctions of the double-well potential and its eigenvalues.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-12-30T22:04:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quartic anharmonic oscillator",
      "quantum quartic single-well anharmonic oscillator",
      "anharmonic oscillator eigenfunction",
      "double-well anharmonic oscillator",
      "uniformly-accurate approximation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}