Some classes of finite-dimensional ladder operators
Fabio Bagarello, Antonino Faddetta, Francesco Oliveri · Journal of Physics A Mathematical and Theoretical · 2025
Abstract We introduce and study some special classes of ladder operators in finite-dimensional Hilbert spaces. In particular we consider a truncated version of quons, their pseudo-version, and a third family of operators acting on a closed chain. In this latter situation, we discuss the existence of what could be considered discrete coherent states, as suitable eigenvectors of the annihilation operator of the chain. We see that, under reasonable assumptions, a resolution of the identity can be recovered, involving these states, together with a biorthogonal family of vectors, which turn out to be eigenstates of the raising operator of the chain.