Exact solutions of a pseudoharmonic oscillator and a family of isospectral potentials are investigated in spherical coordinates. The entropic moment, generalized quantum similarity index, and some quantum information measures are investigated analytically and numerically for two density functions of two quantum systems with same energy and one quantum system with different energies. Analytical results are compared for 19 selected molecules and verified by some physical and artificial values of the spectroscopic parameters.

We study the shape LMC (López-Ruiz, Mancini and Calvet), Fisher-Shannon (FS) andCramér-Rao (CR) complexities of two families of orthogonal functions associated with the solutions of isospectral deformations of the Pöschl-Teller and Harmonic oscillator potentials. We have compared the behavior of these complexities for the orthogonal functions with the complexities associated with Pöschl-Teller and Harmonic oscillator potentials whose solutions are given in terms of the classical orthogonal polynomials. All these complexities are discussed in terms of the quantum number n and isospectrality parameter λ. K E Y W O R D SCramér-Rao complexity, Fisher-Shannon complexity, LMC complexity 1 | INTRODUCTION Application of statistical measures in physical as well as in social sciences has a role of growing importance. There exists a vast literature on the use of various measures of complexity in different contexts for example, dynamical systems, cellular automata, neural networks, social sciences, complex molecules, geophysical and astrophysical processes etc. In particular, López-Ruiz, Mancini, and Calvet (LMC) complexity [1][2][3][4][5] has been computed in position and momentum spaces [6] for the density functions of the hydrogen-like atoms and the isotropic harmonic oscillator. [7,8] The LMC complexity is defined as a product of two factors-one of which is a measure of the disequilibrium, that is, it quantifies the departure of the probability density from uniformity while the other one is the Shannon entropy which is a measure of uncertainty or randomness. [9] The modified LMC complexity, that is, the shape LMC is the product of the Shannon length and the disequilibrium [2,4,5] and have been studied in different contexts. [4,[10][11][12][13][14] Another measure of complexity is the Fisher-Shannon (FS) complexity. [15][16][17][18] It is defined as the product of the Fisher information [19] and Shannon entropic power. The LMC and the FS complexity measures have been applied in different fields of physics such as multi electron systems in position and momentum spaces, [20,21] analysis of signals, [15] electron correlation, [16] atomic systems and ionization processes [18,22] and in quantum mechanics. [7,8,23] The third complexity measure that we shall study is the Cramér-Rao (CR) complexity which is defined as the product of the Fisher information and the variance of the density function measuring the degree of deviation from the mean value. [20,22,24,25] The three complexities mentioned above share a set of characteristics, namely, they are (a) dimensionless (b) bounded below by unity, and (c) minimum for two extreme distributions which correspond to perfect order and maximum disorder. Also they are invariant under replication, translation and scaling transformation. [4,[26][27][28][29][30] It is to be noted that various information theoretic measures of uncertainty and complexity have been studied in great detail for the wellknown classical orthogonal polynomials which generate solutions of problems like the Harm...

We studied exact solutions and spectrum analysis of the pseudoharmonic oscillator in the presence of θ‐dependent scalar potential and the sum of two vector potentials Dirac magnetic monopole and Aharonov‐Bohm field. The effect of the Dirac magnetic monopole (g), Aharonov‐Bohm field (ℱ), the dissociation energy of diatomic molecules (D e), equilibrium intermolecular separation (r e), and the reduced mass (μ) on the energy spectrum for some diatomic molecules (CO, NO, N2, CH, H2, and ScH) are analyzed. We compared our results with theoretical experiments of pseudoharmonic oscillator potential in a molecular system.

Exact wave functions are obtained for noncentral Kratzer potential in the presence of Aharonov‐Bohm flux field in terms of associate Laguerre and Jacobi polynomials. The exact form of Rényi entropy and generalized Rényi complexity are determined for positive integral order and , respectively. The narrowest confined and widest spread radial wave functions dominate the localization property of rotational wave functions for the optimum measure of Rényi entropy. The minimum and the maximum values of the Rényi entropy are found for the narrowest confined and widest spread radial wave functions, respectively. Conversely, the narrowest confined and widest spread rotational wave functions dominate the localization property of radial wave functions for the optimum measure of the generalized Rényi and shape Rényi complexities. If the generalized Rényi and shape Rényi complexities are minimum for the narrowest confined rotational wave function, then they will be maximum for the widest spread rotational wave function and vice versa.

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.