$\mathcal{D}$-deformed harmonic oscillators

Abstract

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\mathcal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called $\mathcal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.

in press in International Journal of Theoretical Physics

References in corpus (2)

• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Non Hermitian Operators with Real Spectrum in Quantum Mechanics