Related papers: Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

URL: http://arxiv.org/abs/2408.01397v2
Date: Thu, 22 Aug 2024 20:34:03 GMT
Title: Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
Authors: Aritra Ghosh, Akash Sinha,
Abstract summary: We describe certain 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.
Score: 9.944647907864256
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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