A class of weak pseudo-bosons and their bi-coherent states

TL;DR

This paper extends the theory of weak pseudo-bosons and bi-coherent states, introducing new ladder operators and non-self-adjoint Hamiltonians, with detailed discussion on compatible functions and illustrative examples.

Contribution

It introduces a broader class of pseudo-bosonic ladder operators and constructs new diagonalizable non-self-adjoint Hamiltonians, advancing the mathematical framework of pseudo-bosonic systems.

Findings

Generalized pseudo-bosonic ladder operators

Constructed new non-self-adjoint Hamiltonians

Analyzed the role of compatible functions

Abstract

In this paper we extend some previous results on weak pseudo-bosons and on their related bi-coherent states. The role of {\em compatible} functions is discussed in details, and some examples are considered. The pseudo-bosonic ladder operators analysed in this paper generalize significantly those considered so far, and a class of new diagonalizable manifestly non self-adjoint Hamiltonians are deduced.