Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
Abstract
In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional potential to an imaginary-valued gauge field, it is possible to obtain certain pseudo-Hermitian extensions of the original (Hermitian) problem. In particular, it is pointed out that the Swanson oscillator arises as such an extension of the quantum harmonic oscillator. For the pseudo-Hermitian extensions of the harmonic and isotonic oscillators, we explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations.
Keywords
Cite
@article{arxiv.2408.01397,
title = {Pseudo-Hermitian extensions of the harmonic and isotonic oscillators},
author = {Aritra Ghosh and Akash Sinha},
journal= {arXiv preprint arXiv:2408.01397},
year = {2025}
}
Comments
Based on talk delivered at the Xth International Workshop on New Challenges in Quantum Mechanics: Graphene, Supersymmetry, and Mathematical Physics (2024); v2: Some errors corrected; v3: Final version