Exploring Pseudo-Hermitian Extensions in Quantum Mechanics

Recent research by Aritra Ghosh and Akash Sinha explores the concept of pseudo-Hermitian extensions of the harmonic and isotonic oscillators, which are significant models in quantum mechanics. The authors detail how these extensions can be achieved by coupling the dynamics of a particle in a one-dimensional potential to an imaginary-valued gauge field. This approach allows for the derivation of new wavefunctions and the examination of their intertwining relations.

The study highlights that the Swanson oscillator is a notable example of such an extension of the quantum harmonic oscillator. The findings are crucial as they provide explicit solutions for the wavefunctions in the position representation, which can enhance the understanding of quantum systems and their behaviors under different conditions.

The implications of this research extend to various fields within quantum physics, potentially influencing future studies on quantum systems and their applications. The authors presented their work at the Xth International Workshop on New Challenges in Quantum Mechanics, indicating its relevance in ongoing discussions in the field.

For further details, the paper titled "Pseudo-Hermitian extensions of the harmonic and isotonic oscillators" can be accessed here.