# Coherent states for nonlinear harmonic oscillator and some of its properties

## Abstract

A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.

- Authors:

- School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)

- Publication Date:

- OSTI Identifier:
- 22479690

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; CORRELATION FUNCTIONS; EIGENSTATES; EIGENVALUES; HARMONIC OSCILLATORS; NONLINEAR PROBLEMS; OSCILLATORS; STATISTICS

### Citation Formats

```
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk.
```*Coherent states for nonlinear harmonic oscillator and some of its properties*. United States: N. p., 2015.
Web. doi:10.1063/1.4922606.

```
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, & Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk.
```*Coherent states for nonlinear harmonic oscillator and some of its properties*. United States. doi:10.1063/1.4922606.

```
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk, and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk. Mon .
"Coherent states for nonlinear harmonic oscillator and some of its properties". United States.
doi:10.1063/1.4922606.
```

```
@article{osti_22479690,
```

title = {Coherent states for nonlinear harmonic oscillator and some of its properties},

author = {Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk and Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk},

abstractNote = {A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.},

doi = {10.1063/1.4922606},

journal = {Journal of Mathematical Physics},

number = 6,

volume = 56,

place = {United States},

year = {Mon Jun 15 00:00:00 EDT 2015},

month = {Mon Jun 15 00:00:00 EDT 2015}

}