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arXiv · 2408.01397

Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

Aritra Ghosh·Akash Sinha
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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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Aritra Ghosh, Akash Sinha. 2024-08-02. Pseudo-Hermitian extensions of the harmonic and isotonic oscillators. https://doi.org/10.1088/1742-6596%2F2986%2F1%2F012004

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