Coherent states of Krawtchouk oscillator and beyond

TL;DR

This paper constructs and analyzes coherent states for a generalized Krawtchouk oscillator, comparing them with existing variants and definitions, contributing to the understanding of nonlinear quantum oscillators.

Contribution

It introduces a new approach to defining coherent states for the Krawtchouk oscillator and compares these with previous models from different perspectives.

Findings

Constructed generalized Krawtchouk oscillator and its coherent states.

Compared new coherent states with existing variants.

Provided insights into phase properties of the oscillator.

Abstract

In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained for another variant of Krawtchouk oscillator in the paper [N.M.Atakishiev and S.K.Suslov, Difference analogs of the harmonic oscillator, Teor. Mat. Fiz., 85, 64-73 (1990)] from other point of view. Our definition of coherent states is close to one given in [B.Roy and P.Roy, Phase properties of a new nonlinear coherent state, quant-ph/0002043] This investigation is partially supported by RFBR grant No 06-01-00451