Inverted oscillator: pseudo hermiticity and coherent states
DOI:
https://doi.org/10.31349/RevMexFis.69.010402Keywords:
Inverted harmonic oscillator; harmonic HamiltonianAbstract
It is known that the standard and the inverted harmonic oscillator are different. Replacing thus ω by ±iω in the regular oscillator is necessary going to give the inverted oscillator H^{r}. This replacement would lead to anti- PT-symmetric harmonic oscillator Hamiltonian (∓iH^{os}). The pseudo-hermiticity relation has been used here to relate the anti-PT-symmetric harmonic Hamiltonian to the inverted oscillator. By using a simple algebra, we introduce the ladder operators describing the inverted harmonic oscillator to reproduce the analytical solutions.We construct the inverted coherent states which minimize the quantum mechanical uncertainty between the position and the momentum. This paper is dedicated to the memory of Omar Djemli and Nouredinne Mebarki who died due to covid 19.
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Copyright (c) 2023 Rahma Zerimeche, Rostom Moufok, Nadjat Amaouche, Mustapha Maamache
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