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arXiv · 2211.09957

Quantum inverted harmonic potential

C. Yuce
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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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C. Yuce. 2022-11-16. Quantum inverted harmonic potential. https://doi.org/10.1088/1402-4896%2Fac1087

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