On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator

TL;DR

This paper constructs various types of nonlinear coherent states for a specific exactly solvable nonlinear oscillator, exploring their properties and extending the analysis to a position-dependent mass Schrödinger equation.

Contribution

It introduces new nonlinear coherent states for a middle-ground nonlinear oscillator and analyzes their properties, including nonclassical features, with explicit state expressions.

Findings

Constructed nonlinear coherent states for the nonlinear oscillator.

Analyzed nonclassical properties of these states.

Extended the construction to position-dependent mass systems.

Abstract

We construct nonlinear coherent states or f-deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Cari\~nena J F et al, J. Phys. A: Math. Theor. 41, 085301 (2008)). The deformed annihilation and creation operators which are required to construct the nonlinear coherent states in the number basis are obtained from the solution of the Schr\"odinger equation. Using these operators, we construct generalized intelligent states, nonlinear coherent states, Gazeau-Klauder coherent states and the even and odd nonlinear coherent states for this newly solvable system. We also report certain nonclassical properties exhibited by these nonlinear coherent states. In addition to the above, we consider position dependent mass Schr\"odinger equation associated with this solvable nonlinear oscillator and construct nonlinear coherent states, Gazeau-Klauder coherent states and the even and odd nonlinear coherent states for it. We also give explicit expressions of all these nonlinear coherent states by considering a mass profile which is often used for studying transport properties in semiconductors.