Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

Autor:	Ghosh, Aritra, Sinha, Akash
Rok vydání:	2024
Předmět:	Quantum Physics Mathematical Physics
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
Externí odkaz:	http://arxiv.org/abs/2408.01397 Zobrazit plný text záznamu View this record from Arxiv