### Abstract

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

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A |

Volume | 473 |

Publication status | Published - 2017 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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

Research output: Contribution to journal › Article

*PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A*, vol. 473, pp. 1-13.

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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 -