2021/02/10 by Bagarello, Fabio
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2102.05614
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 \Lc2(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 \citebag2010jmp. The results deduced here belong to the same distributional approach to pseudo-bosons first proposed in \citebag2020JPA.