Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909580824412160 |
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| author | Ghosh, Aritra Sinha, Akash |
| author_facet | Ghosh, Aritra Sinha, Akash |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudo-Hermitian extensions of the harmonic and isotonic oscillators Ghosh, Aritra Sinha, Akash Quantum Physics Mathematical Physics 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. |
| title | Pseudo-Hermitian extensions of the harmonic and isotonic oscillators |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2408.01397 |