{
  "id": "2103.03306",
  "version": "v1",
  "published": "2021-03-04T20:23:10.000Z",
  "updated": "2021-03-04T20:23:10.000Z",
  "title": "Temperature as perturbation in quantum mechanics",
  "authors": [
    "Ashkan Shekaari",
    "Mahmoud Jafari"
  ],
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech"
  ],
  "abstract": "The perturbative approach was adopted to develop a temperature-dependent version of non-relativistic quantum mechanics in the limit of low-enough temperatures. A generalized, self-consistent Hamiltonian was therefore constructed for an arbitrary quantum-mechanical system in a way that the ground-state Hamiltonian turned out to be just a limiting case at absolute zero. The weak-coupling term connecting the system of interest and its immediate environment was accordingly treated as the perturbation. Applying the obtained generalized Hamiltonian to some typical quantum systems with exact zero-temperature solutions, including the free particle in a box, the free particle in vacuum, and the harmonic oscillator, up to the first order of self-consistency, therefore corrected their associated Hamiltonians, energy spectrums, and wavefunctions to be consistent with the low-temperature limit. Further investigation revealed some kind of quantum tunneling effect by a residual probability for the free particle in a box, as a chief consequence of thermally coupling to the reservoir. The possible effects of thermal environment on the main properties of the wavefunctions were also thoroughly examined and discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-04T20:23:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free particle",
      "perturbation",
      "non-relativistic quantum mechanics",
      "exact zero-temperature solutions",
      "main properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}