${\cal D}$-deformed harmonic oscillators

TL;DR

This paper systematically analyzes various deformations of two-dimensional harmonic oscillators using the framework of $ ext{D}$-pseudo bosons, leading to exactly solvable non-Hermitian models that encompass many previously studied cases.

Contribution

It introduces a unified framework for exactly solvable deformed harmonic oscillators via $ ext{D}$-pseudo bosons, connecting and extending existing models.

Findings

All models are exactly solvable with explicit eigenvalues and eigenvectors.

Several previously introduced models are shown to fit into the $ ext{D}$-pseudo boson scheme.

The framework simplifies the analysis of non self-adjoint Hamiltonians in quantum mechanics.

Abstract

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-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 $\cal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.