Yadav, S., Shekhar, S., Bagchi, B., & Mandal, B. P. (2024). Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model. arXiv preprint arXiv:2406.09164v2.
This research paper aims to demonstrate the existence of zero-energy normalizable solutions for a class of QES rational potentials within the framework of a rationally extended many-body truncated Calogero-Sutherland (TCS) model.
The authors utilize algebraic techniques based on the so(2, 1) potential algebra for the Schrödinger equation. They employ a point canonical transformation and analyze three distinct types of potentials emerging from the so(2, 1) structure, each having the same eigenvalues. By restricting the coupling parameters for each case, they investigate the existence of regular, normalizable wavefunctions at zero energy.
The research successfully demonstrates the existence of zero-energy normalizable solutions for a specific class of QES rational potentials within the extended TCS model. This finding expands the understanding of solvable potentials in quantum mechanics and highlights the significance of the so(2, 1) potential algebra and point canonical transformations in uncovering such solutions.
This research contributes to the field of quantum mechanics by expanding the repertoire of solvable potentials and providing insights into the behavior of quantum systems at zero energy. The findings have implications for understanding quantum confinement and the properties of interacting particle systems.
The study focuses on a specific class of QES potentials within the extended TCS model. Further research could explore the applicability of the presented methodology to other quantum mechanical models and investigate the physical implications of the identified zero-energy states in greater detail.
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by Satish Yadav... alle arxiv.org 10-08-2024
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