{
  "id": "2406.10925",
  "version": "v1",
  "published": "2024-06-16T13:05:20.000Z",
  "updated": "2024-06-16T13:05:20.000Z",
  "title": "Determination of the Hamiltonian from the Equations of Motion with Illustration from Examples",
  "authors": [
    "Chung-Ru Lee"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first order evolutionary equations in the phase space coordinates. We state the criterion on the evolution matrix for a Hamiltonian to exist. In addition, the proof is constructive and an explicit Hamiltonian with accompanied symplectic structure can be obtained. As an application, we will study a class of PT-symmetric systems for illustration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-16T13:05:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determination",
      "illustration",
      "first order evolutionary equations",
      "phase space coordinates",
      "matrix factorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}