Quantum inverted harmonic potential

• URL: http://arxiv.org/abs/2211.09957v1
• Date: Wed, 16 Nov 2022 02:03:42 GMT
• Title: Quantum inverted harmonic potential
• Authors: C. Yuce
• Abstract summary: We show that uncertainty in position of a particle under the inverted harmonic potential can be zero. We obtain a new free particle wave packet using the eigenstates for the inverted harmonic potential.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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