{
  "id": "1908.07876",
  "version": "v1",
  "published": "2019-08-21T13:56:53.000Z",
  "updated": "2019-08-21T13:56:53.000Z",
  "title": "On an optimal potential of Schrödinger operator with prescribed $m$ eigenvalue",
  "authors": [
    "Yavdat Ilyasov",
    "Nurmukhamet Valeev"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential $V_0$ find the closest function $\\hat{V}$ such that $m$ eigenvalues of one-dimensional space Schrodinger operator with potential $\\hat{V}$ would coincide with the given values $ E_1 $, $ \\ldots $, $ E_m \\in \\mathbb {R} $. In our main result, we prove the existence of a solution to this problem, and more importantly, we show that such a solution can be directly found by solving a system of nonlinear differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-21T13:56:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B15",
      "65R32",
      "74J25"
    ],
    "keywords": [
      "schrödinger operator",
      "optimal potential",
      "nonlinear differential equations",
      "eigenvalue",
      "one-dimensional space schrodinger operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}