{
  "id": "1001.1706",
  "version": "v2",
  "published": "2010-01-11T17:20:14.000Z",
  "updated": "2010-06-03T07:27:41.000Z",
  "title": "Eigenstates with the auxiliary field method",
  "authors": [
    "Claude Semay",
    "Bernard Silvestre-Brac"
  ],
  "comment": "Extended version published in J. Phys. A",
  "journal": "J. Phys. A 43 (2010) 265302",
  "doi": "10.1088/1751-8113/43/26/265302",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The auxiliary field method is a powerful technique to obtain approximate closed-form energy formulas for eigenequations in quantum mechanics. Very good results can be obtained for Schr\\\"odinger and semirelativistic Hamiltonians with various potentials, even in the case of many-body problems. This method can also provide approximate eigenstates in terms of well known wavefunctions, for instance harmonic oscillator or hydrogen-like states, but with a characteristic size which depends on quantum numbers. In this paper, we consider two-body Schr\\\"odinger equations with linear, logarithmic and exponential potentials and show that analytical approximations of the corresponding eigenstates can be obtained with the auxiliary field method, with a very good accuracy in some cases.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-03T07:27:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "auxiliary field method",
      "approximate closed-form energy formulas",
      "instance harmonic oscillator",
      "exponential potentials",
      "quantum mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Jul",
      "volume": 43,
      "number": 26,
      "pages": 265302
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43z5302S"
    }
  }
}