The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 23 2 2023 08 23 Investigating and analysis of the properties of coherent states of a deformed nonlinear harmonic oscillator Investigating and analysis of the properties of coherent states of a deformed nonlinear harmonic oscillator 405 417 3410 10.47176/ijpr.23.2.61705 FA Mohsen Daeimohammad Department of Physics, Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 0000-0001-9821-6085 Mohammad Nili Ahmadabadi Department of Mathematics, Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran Journal Article 2023 06 27 In this research, we study the<strong> </strong>coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid. In this research, we study the<strong> </strong>coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid. https://ijpr.iut.ac.ir/article_3410_c6f798b844366ccd65d99bc7f31e0e02.pdf