Superstatistics of Schrödinger equation with pseudo-harmonic potential in external magnetic and Aharanov-Bohm fields

Abstract

In this work, the thermodynamic property of pseudoharmonic potential in the presence of external magnetic and AB fields is investigated. We used effective Boltzmann factor within the superstatistics formalism to obtain the thermodynamic properties such as Helmholtz free energy (F), Internal energy (U), entropy(S) and specific heat (C) of the system. In addition, we discuss the result of the thermodynamic properties of some selected diatomic molecules of 2 2 2 ,, N Cl I and CH using their experimental spectroscopic parameters and that of the variation of the deformation parameter of 0,0.3,0.7 q  . We also illustrated with some graphs for clarity of our results in both cases.

Generalized quantum similarity index: An application to pseudoharmonic oscillator with isospectral potentials in 3D

“…Let us consider the pseudoharmonic oscillator potential [ 1–16 ] where r is the internuclear distance between diatomic molecules. Therefore, the effective pair of isospectral potentials in one dimension is where …”

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

“…Hence, with an approximation to the centrifugal term, interest is geared towards arbitrary -solutions of the radial Schrödinger equation. Arbitrary -solutions play a dominant role in non-relativistic quantum mechanics since the wave function and associated eigenvalues contain all the necessary information for a full description of a quantum system [5][6][7][8]. With the experimental verification of the Schrödinger equation, researchers have devoted much interest in solving the radial Schrödinger equation to obtain bound state solutions with various methods for some potential models [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Theoretic quantum information entropies for the generalized hyperbolic potential

“…In order to ameliorate this difficulty, Qiang and Dong [ 61 ] proposed a proper exact quantization rule for simplification. Motivated by these simplification methods and based on the NU method, [ 16 ] parametric NU method, [ 59 ] and functional analysis method, [ 62 ] Ikot et al [ 20 ] proposed NUFA as a simple and elegant method for solving a second‐order differential equation of the hypergeometric type. This method is as reviewed below.…”

“…The analytical solutions of the Schrödinger equation with different potential models have been investigated by many authors in the literature. [ 11–15 ] Different analytical techniques have been used to obtain either exact or approximate solutions of the Schrödinger equation, such as the Nikiforov‐Uvarov (NU) [ 16 ] method, asymptotic iteration method (AIM), [ 17 ] supersymmetric quantum mechanics, [ 18 ] functional analysis method, [ 19 ] and our newly proposed Nikiforov‐Uvarov and Functional analysis (NUFA) [ 20 ] method. In recent years, many authors have devoted interest in investigating the information‐theoretic measures for quantum mechanical systems.…”