{
  "id": "2309.06605",
  "version": "v1",
  "published": "2023-09-12T21:10:02.000Z",
  "updated": "2023-09-12T21:10:02.000Z",
  "title": "On the complex solution of the Schrödinger equation with exponential potentials",
  "authors": [
    "Javier Garcia"
  ],
  "comment": "22 pages, 3 figures, 5 tables",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the analytical solutions of the Schr\\\"odinger equation with a repulsive exponential potential $\\lambda e^{- r}$, and that with an exponential wall $\\lambda e^r$, both with $\\lambda > 0$. We show that the complex eigenenergies obtained for the latter tend either to those of the former, or to real rational numbers as $\\lambda \\rightarrow \\infty$. In the light of these results, we explain the wrong resonance energies obtained in a previous application of the Riccati-Pad\\'e method to the Schr\\\"odinger equation with a repulsive exponential potential, and further study the convergence properties of this approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-12T21:10:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equation",
      "complex solution",
      "repulsive exponential potential",
      "wrong resonance energies",
      "real rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}