Pseudo-bosons and bi-coherent states out of $\Lc^2(\mathbb{R})$
arXiv:2102.05614
Abstract
In this paper we continue our analysis on deformed canonical commutation relations and on their related pseudo-bosons and bi-coherent states. In particular, we show how to extend the original approach outside the Hilbert space $\Lc^2(\mathbb{R})$, leaving untouched the possibility of defining eigenstates of certain number-like operators, manifestly non self-adjoint, but opening to the possibility that these states are not square-integrable. We also extend this possibility to bi-coherent states, and we discuss in many details an example based on a couple of superpotentials first introduced in \cite{bag2010jmp}. The results deduced here belong to the same distributional approach to pseudo-bosons first proposed in \cite{bag2020JPA}.
Paper in press in the proceedings of the online series of seminars Pseudo-Hermitian Hamiltonians in Quantum Physics (XIX<vPHHQP<XX), (eds. C.M. Bender, F. Correa and A. Fring, Journal of Physics: Conference Series (IoP Publishing))