Coordinate representation for non-Hermitian position and momentum operators

Fabio Bagarello, Francesco Gargano, Salvatore Triolo, Salvatore Spagnolo, Bagarello

Risultato della ricerca: Article

5 Citazioni (Scopus)

Abstract

In this paper, we undertake an analysis of the eigenstates of two non-self-adjoint operators q^q^ and p^p^ similar, in a suitable sense, to the self-adjoint position and momentum operators q^0 q^0 and p^0 p^0 usually adopted in ordinary quantum mechanics. In particular, we discuss conditions for these eigenstates to be biorthogonal distributions, and we discuss a few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non-self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with q^ q^ and p^ p^, based on the so-called quasi *-algebras.
Lingua originaleEnglish
pagine (da-a)1-13
Numero di pagine13
RivistaPROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A
Volume473
Stato di pubblicazionePublished - 2017

Fingerprint

Quantum theory
Algebra
Momentum
momentum
operators
Non-self-adjoint Operator
Operator
Quantum Mechanics
eigenvectors
Alternatives
quantum mechanics
algebra
Strategy
Similarity

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cita questo

Coordinate representation for non-Hermitian position and momentum operators. / Bagarello, Fabio; Gargano, Francesco; Triolo, Salvatore; Spagnolo, Salvatore; Bagarello.

In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A, Vol. 473, 2017, pag. 1-13.

Risultato della ricerca: Article

Bagarello, F, Gargano, F, Triolo, S, Spagnolo, S & Bagarello 2017, 'Coordinate representation for non-Hermitian position and momentum operators', PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A, vol. 473, pagg. 1-13.
Bagarello F, Gargano F, Triolo S, Spagnolo S, Bagarello. Coordinate representation for non-Hermitian position and momentum operators. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. 2017;473:1-13.
Bagarello, Fabio ; Gargano, Francesco ; Triolo, Salvatore ; Spagnolo, Salvatore ; Bagarello. / Coordinate representation for non-Hermitian position and momentum operators. In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. 2017 ; Vol. 473. pagg. 1-13.
@article{0807ee6bbf9c49918ea7e8d475306d34,
title = "Coordinate representation for non-Hermitian position and momentum operators",
abstract = "In this paper, we undertake an analysis of the eigenstates of two non-self-adjoint operators q^q^ and p^p^ similar, in a suitable sense, to the self-adjoint position and momentum operators q^0 q^0 and p^0 p^0 usually adopted in ordinary quantum mechanics. In particular, we discuss conditions for these eigenstates to be biorthogonal distributions, and we discuss a few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non-self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with q^ q^ and p^ p^, based on the so-called quasi *-algebras.",
author = "Fabio Bagarello and Francesco Gargano and Salvatore Triolo and Salvatore Spagnolo and Bagarello",
year = "2017",
language = "English",
volume = "473",
pages = "1--13",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "0080-4630",
publisher = "The Royal Society",

}

TY - JOUR

T1 - Coordinate representation for non-Hermitian position and momentum operators

AU - Bagarello, Fabio

AU - Gargano, Francesco

AU - Triolo, Salvatore

AU - Spagnolo, Salvatore

AU - Bagarello, null

PY - 2017

Y1 - 2017

N2 - In this paper, we undertake an analysis of the eigenstates of two non-self-adjoint operators q^q^ and p^p^ similar, in a suitable sense, to the self-adjoint position and momentum operators q^0 q^0 and p^0 p^0 usually adopted in ordinary quantum mechanics. In particular, we discuss conditions for these eigenstates to be biorthogonal distributions, and we discuss a few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non-self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with q^ q^ and p^ p^, based on the so-called quasi *-algebras.

AB - In this paper, we undertake an analysis of the eigenstates of two non-self-adjoint operators q^q^ and p^p^ similar, in a suitable sense, to the self-adjoint position and momentum operators q^0 q^0 and p^0 p^0 usually adopted in ordinary quantum mechanics. In particular, we discuss conditions for these eigenstates to be biorthogonal distributions, and we discuss a few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non-self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with q^ q^ and p^ p^, based on the so-called quasi *-algebras.

UR - http://hdl.handle.net/10447/241108

UR - http://rspa.royalsocietypublishing.org/content/473/2205/20170434

M3 - Article

VL - 473

SP - 1

EP - 13

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

ER -

Accesso al documento