Inverted oscillator: pseudo hermiticity and coherent states

It is known that the standard and inverted harmonic oscillator are different. Replacing thus ω by ±iω in regular necessary going to give H^{r}. This replacement would lead anti- PT-symmetric Hamiltonian (∓iH^{os}). The pseudo-hermiticity relation has been used here relate anti-PT-symmetric oscillator. By using a simple algebra, we introduce ladder operators describing reproduce analytical solutions.We construct coherent states which minimize quantum mechanical uncertainty between position momentum. paper dedicated memory of Omar Djemli Nouredinne Mebarki who died due covid 19.