{
  "annotation_id": "40b9b92b-1776-419c-9334-51d15a5ce50b",
  "date_created": "2026-03-02T18:02:47.944000Z",
  "date_modified": "2026-03-02T18:02:47.944000Z",
  "file_hash": "bdd462bda11fcb56f378d2eeeeab46bb46a56bb7804894a44bf498ff5b55d2c5",
  "private": false,
  "record": {
    "abstract": "We discuss a new relation between the low lying Schroedinger wave function of\na particle in a one-dimentional potential V and the solution of the\ncorresponding Hamilton-Jacobi equation with -V as its potential. The function V\nis $\\geq 0$, and can have several minina (V=0). We assume the problem to be\ncharacterized by a small anhamornicity parameter $g^{-1}$ and a much smaller\nquantum tunneling parameter $\\epsilon$ between these different minima.\nExpanding either the wave function or its energy as a formal double power\nseries in $g^{-1}$ and $\\epsilon$, we show how the coefficients of\n$g^{-m}\\epsilon^n$ in such an expansion can be expressed in terms of definite\nintegrals, with leading order term determined by the classical solution of the\nHamilton-Jacobi equation. A detailed analysis is given for the particular\nexample of quartic potential $V={1/2}g^2(x^2-a^2)^2$.",
    "arxiv_id": "quant-ph/9910047",
    "authors": [
      "R. Friedberg",
      "T. D. Lee",
      "W. Q. Zhao"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/BF03035922",
    "title": "Relations Between Low-lying Quantum Wave Functions and Solutions of the   Hamilton-Jacobi Equation",
    "url": "https://arxiv.org/abs/quant-ph/9910047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "419efa70-9c49-45f2-9000-57b1b9d3b44c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}