arXiv subjects

A. M. Jafarova

Publications and source records attributed to A. M. Jafarova.

3 recordsLinked to original sources

arXiv2023

The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.

quant-ph↗

arXiv2022

The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass

The phase space representation for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. We have found the Husimi distribution function for the stationary states of the oscillator model under consideration for both cases without and with the applied external homogeneous field. The obtained function is expressed through the double sum of the parabolic cylinder function. Different special cases and the limit relations are discussed, too.

quant-ph↗

arXiv2015

The $\mathfrak{su}(2)$ Krawtchouk oscillator model under the ${\cal C}{\cal P}$ deformed symmetry

We define a new algebra, which can formally be considered as a ${\cal C}{\cal P}$ deformed $\mathfrak{su}(2)$ Lie algebra. Then, we present a one-dimensional quantum oscillator model, of which the wavefunctions of even and odd states are expressed by Krawtchouk polynomials with fixed $p=1/2$, $K_{2n}(k;1/2,2j)$ and $K_{2n}(k-1;1/2,2j-2)$. The dynamical symmetry of the model is the newly introduced $\mathfrak{su}(2)_{{\cal C}{\cal P}}$ algebra. The model itself gives rise to a finite and discrete spectrum for all physical operators (such as position and momentum). Among the set of finite oscillator models it is unique in the sense that any specific limit reducing it to a known oscillator models does not exist.

math-ph↗