{
  "id": "0705.0730",
  "version": "v1",
  "published": "2007-05-05T06:24:22.000Z",
  "updated": "2007-05-05T06:24:22.000Z",
  "title": "Reciprocal Symmetry and Unified Classico-Quantum Oscillator And Consistency between a Particle in a Potential Well and a Harmonic Oscillator",
  "authors": [
    "Mushfiq Ahmad",
    "Muhammad O. G. Talukder"
  ],
  "comment": "6 pages, no figure",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The function exp(iwt) describes an oscillating motion. Energy of the oscillator is proportional to the square of w. exp(iwt) is the solution of a differential equation. We have replaced this differential equation by the corresponding finite-time difference equation with d as the smallest span of time. We have, then, symmetrized the equation so that it remains invariant under the change d going to -d. This symmetric equation has solutions in pairs. The angular speed w is modified to w' or w\". w' contains a part with an integer. w\" contains a part with a half-integer. This corresponds to quantum mechanical oscillator energy levels. F= a.exp(iwt) describes oscillation between -a and +a. If we make w=0, F describes free oscillation between -a and +a. Reciprocal symmetric oscillator, thus, unifies quantum and classical harmonic oscillators on one hand, and a harmonic oscillator and a free particle in a potential well on the other hand. No quantum mechanical postulates are involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-05T06:24:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic oscillator",
      "unified classico-quantum oscillator",
      "reciprocal symmetry",
      "consistency",
      "differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0730A"
    }
  }
}