{
  "id": "2006.09544",
  "version": "v1",
  "published": "2020-06-16T22:18:25.000Z",
  "updated": "2020-06-16T22:18:25.000Z",
  "title": "Supersymmetry of $\\mathscr{PT}$- symmetric tridiagonal Hamiltonians",
  "authors": [
    "M. W. AlMasri"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "The notion of pseudo-Hermiticity is introduced in the context of supersymmetric tridiagonal Hamiltonians. Our formalism works for Hermitian and non-Hermitian Hamiltonians with real or complex-conjugate pair eigenvalues . We find the relation between matrix elements of the Hamiltonian $H$ and its supersymmetric partner $H^{+}$ in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to $H^{+}$ can be recovered from those polynomials arising from the same problem for $H$ with the help of kernel polynomials. We apply our formalism to the case of shifted $\\mathscr{PT}$-symmetric Morse oscillator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T22:18:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetry",
      "supersymmetric tridiagonal hamiltonians",
      "complex-conjugate pair eigenvalues",
      "eigenstate expansion problem",
      "symmetric morse oscillator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}