Tridiagonality, supersymmetry and non self-adjoint Hamiltonians

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Abstract

In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.
Original languageEnglish
Number of pages17
JournalJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume52
Publication statusPublished - 2019

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Supersymmetry
recursive functions
Hamiltonians
factorization
supersymmetry
eigenvectors
Squeezed States
Recursion Formula
Tridiagonal matrix
Factorization

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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title = "Tridiagonality, supersymmetry and non self-adjoint Hamiltonians",
abstract = "In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.",
author = "Fabio Bagarello and Francesco Gargano and Federico Roccati and Bagarello",
year = "2019",
language = "English",
volume = "52",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
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AB - In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.

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JO - Journal of Physics A: Mathematical and Theoretical

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