Pseudo-Hermitian extensions of the harmonic and isotonic oscillators
Autor: | Ghosh, Aritra, Sinha, Akash |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: Based on talk delivered at the Xth International Workshop on New Challenges in Quantum Mechanics: Graphene, Supersymmetry, and Mathematical Physics (2024) |
Databáze: | arXiv |
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