{
  "id": "2310.15536",
  "version": "v1",
  "published": "2023-10-24T05:44:21.000Z",
  "updated": "2023-10-24T05:44:21.000Z",
  "title": "Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential",
  "authors": [
    "Keiichi Kato",
    "Wataru Nakahashi",
    "Yukihide Tadano"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study non-smoothness of the fundamental solution for the Schr\\\"{o}dinger equation with a spherically symmetric and super-quadratic potential in the sence that $V(x)\\geq C|x|^{2+\\varepsilon}$ at infinity with constants $C>0 $ and $\\varepsilon>0$. More precisely, we show the fundamental solution $E(t,x,y)$ does not belong to $C^{1}$ as a function of $(t,x,y)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-24T05:44:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10"
    ],
    "keywords": [
      "fundamental solution",
      "spherically symmetric potential",
      "schrödinger equations",
      "study non-smoothness",
      "super-quadratic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}