{
  "id": "0806.2020",
  "version": "v1",
  "published": "2008-06-12T08:42:03.000Z",
  "updated": "2008-06-12T08:42:03.000Z",
  "title": "Extensions of the auxiliary field method to solve Schrödinger equations",
  "authors": [
    "Bernard Silvestre-Brac",
    "Claude Semay",
    "Fabien Buisseret"
  ],
  "journal": "J. Phys. A: Math. Theor. 41 (2008) 425301",
  "doi": "10.1088/1751-8113/41/42/425301",
  "categories": [
    "quant-ph",
    "physics.comp-ph"
  ],
  "abstract": "It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schr\\\"{o}dinger equation. This technique can generate the spectrum associated with an arbitrary potential $V(r)$ starting from the analytically known spectrum of a particular potential $P(r)$. In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of $P(r)$. The method is extended in order to find accurate analytical energy formulae for radial potentials of the form $a P(r)+V(r)$, and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-12T08:42:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "auxiliary field method",
      "schrödinger equations",
      "extensions",
      "accurate analytical energy formulae",
      "general important properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Oct",
      "volume": 41,
      "number": 42,
      "pages": 425301
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41P5301S"
    }
  }
}