Effects of magnetic and Aharonov–Bohm flux fields on information entropy with modified Kratzer plus screened Coulomb potential for selected diatomic molecules
Cecilia N. Isonguyo, Eno E. Ituen, I. B. Okon, M. E. Udoh, Akaninyene Daniel Antia, Akpan N. Ikot
The Shannon information entropy for scandium fluoride (ScF) and hydrogen (H2) molecules in the presence of magnetic and Aharanov–Bohm (AB) fields with modified Kratzer plus screened Coulomb potential in the position and momentum coordinate is investigated. The wavefunction and probability density are obtained by solving the two-dimensional (2D) Schrödinger wave equation using the Nikiforov–Uvarov functional analysis method and then applied to calculate the Shannon entropy. The graphical behaviour of the 2D wavefunction and probability density is showcased. Our results depict the effects of the external fields on Shannon entropy for ScF and (H2), the negative values of the position Shannon entropies obtained imply higher localisation of the particles and molecules indicating more stability of the system. Another interesting part of this work is that Bialynicki–Birula–Mycielski inequality is tested and proven bounded for both diatomic molecules. A few to mention, this research will enhance the apprehension of the dynamics of quantum molecules and systems subjected to external fields, quantum information signal processing and communication.
The Shannon information entropy for scandium fluoride (ScF) and hydrogen (H2) molecules in the presence of magnetic and Aharanov–Bohm (AB) fields with modified Kratzer plus screened Coulomb potential in the position and momentum coordinate is investigated. The wavefunction and probability density are obtained by solving the two-dimensional (2D) Schrödinger wave equation using the Nikiforov–Uvarov functional analysis method and then applied to calculate the Shannon entropy. The graphical behaviour of the 2D wavefunction and probability density is showcased. Our results depict the effects of the external fields on Shannon entropy for ScF and (H2), the negative values of the position Shannon entropies obtained imply higher localisation of the particles and molecules indicating more stability of the system. Another interesting part of this work is that Bialynicki–Birula–Mycielski inequality is tested and proven bounded for both diatomic molecules. A few to mention, this research will enhance the apprehension of the dynamics of quantum molecules and systems subjected to external fields, quantum information signal processing and communication.
In this research article, the influence of magnetic and Aharonov-Bohm flux fields on Shannon entropy with improved Kratzer potential for Scandium fluoride (ScF) and hydrogen (H2) molecules are studied analytically and numerically for three low-lying states. The wave function and probability density which controls the chemical and physical properties of atomic and molecular systems have been obtained by solving the Schrodinger wave equation coupled with charged particle Hamiltonian via the Nikiforov-Uvarov functional analysis method. The total normalized wave function was expressed in terms of the hypergeometric function of Jacobi polynomials and then utilized to evaluate the Shannon entropy for two diatomic molecules in position and momentum spaces. The wave function and electronic densities were graphically analyzed. Our numerical results of Shannon entropies sum as applied to ScF and H2 were verified to obey the Shannon-entropy-based uncertainty relation. Observations from our results also reveal negative values of Shannon entropies in the position coordinates depicting high localization of particles and stability. In Addition, the effects of the external fields on the quantum systems were observed to influence the quantum information-theoretic measure by small decrements in the Shannon entropy values when compared to the case of the absence of the external fields, indicating a further improvement in the localization of particles and system's stability. This work has applications in atomic and molecular dynamic, molecular drug design, nanostructure processes, information technology, amongst others.
In this paper, Fisher and Shannon information entropies in two-dimensional spaces were analysed for hydrogen diatomic molecules using a non-central exponential-type potential, both in the presence and absence of magnetic and Aharanov-Bohm (AB) flux fields. By solving the two-dimensional Schrödinger equation in the presence of charged Hamiltonian using the parametric Nikiforov-Uvarov (NU) method, we obtained numerical solutions for different potential depths for Fisher and Shannon information entropies. These results adhere to Bialynicki-Birula and Mycielski (BBM) and Fisher-based inequalities. The findings have significant applications in chemical physics, aiding in the analysis of molecular electronic properties, stability and reactivity under varying external influences. Additionally, the study contributes to quantum information by offering insights into the localisation and delocalisation phenomena, with direct applications to quantum computation, entanglement, and communication technologies.
In this work, we study an approximate bound state solution of a 2D Schrodinger equation under the influence of external magnetic and Aharonov–Bohm (AB) fields with Hellmann plus screened Kratzer potential (HPSKP) using the Nikiforov–Uvarov-functional- analysis method (NUFA). We obtained the normalised wave function expressed in terms of the Jacobi polynomial. The energy spectra were also obtained in closed form and used to study the energy levels of hydrogen and chromium hydride molecules. The partition function was evaluated using Poisson’s summation approach while other thermomagnetic properties such as free energy, mean energy, entropy, heat capacity, magnetisation, magnetic susceptibility, persistent current at zero and finite temperatures were evaluated analytically.
In the present study, the improved screened Kratzer potential (ISKP) is investigated in the presence of external magnetic and Aharanov-Bohm (AB) fields within the framework of non-relativistic quantum mechanics. The Schrodinger equation is solved via the Nikiforov-Uvarov Functional Analysis (NUFA) method and the energy spectra and the corresponding wave function for the ISKP in the presence of external magnetic fields are obtained in a closed form. The obtained energy spectra are used to study some selected diatomic molecules. It is observed that the present of the magnetic and AB fields removes the degeneracy for different values of the control parameter. The thermodynamic and magnetic properties of the ISKP in the present of the magnetic and AB fields are also evaluated. The effects of the control potential parameter on the thermodynamic and magnetic properties of the selected diatomic molecules are discussed.
In this study, the modified Kratzer energy-dependent screened Coulomb potential is analyzed in the presence of external magnetic and Aharonov–Bohm (AB) flux fields. The Schrödinger equation is solved using the Nikiforov–Uvarov Functional Analysis (NUFA) method, yielding closed-form expressions for the energy eigenvalues and the corresponding wavefunctions. These solutions are applied to investigate the magnetic properties of the titanium hydride (TiH) diatomic molecule, including the partition function, magnetization, magnetic susceptibility, and persistent current. The effects of the slope parameter are examined in detail and found to play a significant role in controlling the magnitude, ordering, and convergence behavior of all magnetic observables. Negative slope values enhance the magnetic and thermodynamic responses of the system, while positive slope values suppress them, with the zero-slope case acting as an intermediate regime. The magnetic field induces divergence and saturation effects, whereas the AB-flux field governs sharp transitions, minima, and convergence characteristics. Overall, the results demonstrate that both the slope parameter and external fields provide effective mechanisms for tuning the magnetic behavior of the TiH diatomic molecule.
Abstract Attempts to understand the behaviour of various quantum systems are still become interest for many researchers in recent years. While experimentation is too complicated to be done, analytical mathematical approach is become a reliable choice. This approach is using potential functions or models as representations of the real quantum system, such as physical force interactions within a molecule. In this study, the new combination model of screened Kratzer and screened Eckart potentials is investigated under the non-relativistic quantum mechanics framework. These potentials are well-suited for modelling atomic interactions in diatomic molecules. The primary objective is to examine how these interactions are affected by the presence of external magnetic fields. Using a specific form of the Schro dinger equation, both the energy eigenfunction and the wave function have been derived. The Nikiforov-Uvarov Functional Analysis (NUFA) method was employed for this derivation. Additionally, several thermodynamic properties were obtained from the energy equation using numerical methods. Selected diatomic molecule data were used in the computations to demonstrate the effect of the magnetic field. A detailed analysis was performed through graphical representations, revealing that an increase in the magnetic field or the associated Aharonov-Bohm (AB) flux enhances and splits the energy spectra. The effects on thermodynamic properties vary across different molecules and conditions, but overall, the magnetic field increases the thermodynamic properties of the molecules.