A generalized statistical complexity based on Rényi entropy of a noncommutative anisotropic oscillator in a homogeneous magnetic field

We calculate the shape Rényi and generalized Rényi complexity of a noncommutative anisotropic harmonic oscillator in a homogeneous magnetic field. To do so, we first obtain the Rényi entropy in position and momentum spaces of the exact normalized wave functions. We observe that shape Rényi and generalized Rényi complexities are monotone functions of noncommutative parameter ([Formula: see text]) in some short range in position space. We analyze the effect of the noncommutative parameter, the magnetic field and the anisotropy on shape Rényi and generalized Rényi complexities.

Dirac equation with anisotropic oscillator, quantum E3′ and Holt superintegrable potentials and relativistic generalized Yang–Coulomb monopole system

The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum [Formula: see text], anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang–Coulomb monopole (YCM) superintegrable system (a [Formula: see text] non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.