### Abstract

Original language | English |
---|---|

Pages (from-to) | 145203- |

Number of pages | 20 |

Journal | JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL |

Volume | 50 |

Publication status | Published - 2017 |

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### 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.

Research output: Contribution to journal › Article

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*, vol. 50, pp. 145203-.

}

TY - JOUR

T1 - Hamiltonians defined by biorthogonal sets

AU - Bellomonte, Giorgia

AU - Bagarello, Fabio

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/239224

UR - http://iopscience.iop.org/article/10.1088/1751-8121/aa60ff/pdf

M3 - Article

VL - 50

SP - 145203-

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

ER -