Quantum inverted harmonic potential
Quantum Physics
2025-05-15 v1 General Physics
Abstract
We consider a non-interacting gas under the inverted harmonic potential and present infinitely degenerate non-stationary orthogonal states. We discuss that it has an infinite entropy at the absolute zero temperature. We show that uncertainty in position of a particle under the inverted harmonic potential can be zero as there exists a solution which asymptotes to a Dirac delta function. We obtain a new free particle wave packet using the eigenstates for the inverted harmonic potential. It has unique self-focusing feature and can be used as focusing beam without a lens in optical systems where paraxial approximation is used.
Keywords
Cite
@article{arxiv.2211.09957,
title = {Quantum inverted harmonic potential},
author = {C. Yuce},
journal= {arXiv preprint arXiv:2211.09957},
year = {2025}
}