Inverted oscillator: pseudo hermiticity and coherent states

• URL: http://arxiv.org/abs/2204.10804v1
• Date: Fri, 22 Apr 2022 16:34:42 GMT
• Title: Inverted oscillator: pseudo hermiticity and coherent states
• Authors: Rahma Zerimeche, Rostom Moufok, Nadjat Amaouche and Mustapha Maamache
• Abstract summary: The pseudo-hermiticity relation has been used here to relate the anti-PT-symmetric harmonic Hamiltonian to the inverted oscillator. We construct the inverted coherent states which minimize the quantum mechanical uncertainty between the position and the momentum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is known that the standard and the inverted harmonic oscillator are different. Replacing thus of {\omega} by i{\omega} 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.

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