### Abstract

We show how the notion of pseudo-bosons, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with generalized eigenvectors of the multiplication and of the derivation operators. Connections with the quantum damped harmonic oscillator are also briefly considered.

Original language | English |
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Pages (from-to) | 135201- |

Number of pages | 13 |

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

Volume | 53 |

Publication status | Published - 2020 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Bagarello, F., & Bagarello (2020). Weak pseudo-bosons.

*JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL*,*53*, 135201-.