Hamiltonians defined by biorthogonal sets

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In some recent papers, studies on biorthogonal Riesz bases have found renewed motivation because of their connection with pseudo-Hermitian quantum mechanics, which deals with physical systems described by Hamiltonians that are not self-adjoint but may still have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed in some previous papers. However, in many physical models, one has to deal not with orthonormal bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of G-quasi basis, and we show a series of conditions under which a definition of non-self-adjoint Hamiltonian with purely point real spectra is still possible.
Original languageEnglish
Pages (from-to)145203-
Number of pages20
JournalJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume50
Publication statusPublished - 2017

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Hamiltonians
Riesz Basis
Orthonormal basis
Hilbert space
quantum mechanics
eigenvectors
Point Spectrum
Quantum theory
Hilbert spaces
Physical Model
decomposition
Eigenvalues and eigenfunctions
Quantum Mechanics
Eigenvector
Decomposition
Decompose
Series
Model

All Science Journal Classification (ASJC) codes

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

Cite this

Hamiltonians defined by biorthogonal sets. / Bellomonte, Giorgia; Bagarello, Fabio.

In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, Vol. 50, 2017, p. 145203-.

Research output: Contribution to journalArticle

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