Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field
Edwin Samson Eyube, Paul P. Notani, Umar Wadata, S. D. Najoji, Bako M. Bitrus, Dlama Yabwa, P. U. Tanko
Abstract In this work, the position-dependent mass Schrödinger equation is solved with the Pöschl-Teller-like potential in the presence of magnetic and Aharonov–Bohm (AB) flux fields. The BenDaniel-Duke ambiguity parameter ordering is used to formulate the Hamiltonian operator for the system. An approximate analytical equation of the bound-state energy spectrum is obtained using the parametric Nikiforov-Uvarov solution technique along with a Pekeris-like approximation scheme. With the aid of the obtained equation for the energy levels, analytical formulas of magnetization and magnetic susceptibility at zero-temperature are derived and subsequently used to predict the physical properties of diatomic substances including the ground state H 2 , HCl, CO and LiH molecules. The expression for the bound-state-energy spectrum is used to generate numerical data for the molecules. The computed energy eigenvalues agree with the literature on diatomic molecules. The study revealed that in the absence of the external fields, the energy eigenvalues and magnetic susceptibility of the system are degenerate. However, with only a low intensity AB field, the degeneracy is completely eliminated from the energy states of the molecules.
Abstract In this work, the position-dependent mass Schrödinger equation is solved with the Pöschl-Teller-like potential in the presence of magnetic and Aharonov–Bohm (AB) flux fields. The BenDaniel-Duke ambiguity parameter ordering is used to formulate the Hamiltonian operator for the system. An approximate analytical equation of the bound-state energy spectrum is obtained using the parametric Nikiforov-Uvarov solution technique along with a Pekeris-like approximation scheme. With the aid of the obtained equation for the energy levels, analytical formulas of magnetization and magnetic susceptibility at zero-temperature are derived and subsequently used to predict the physical properties of diatomic substances including the ground state H 2 , HCl, CO and LiH molecules. The expression for the bound-state-energy spectrum is used to generate numerical data for the molecules. The computed energy eigenvalues agree with the literature on diatomic molecules. The study revealed that in the absence of the external fields, the energy eigenvalues and magnetic susceptibility of the system are degenerate. However, with only a low intensity AB field, the degeneracy is completely eliminated from the energy states of the molecules.
In this present work, we study the approximate solution of the Schrodinger equation with hyperbolic function position-dependent mass for a symmetrical Modified Poschl-Teller potential. We consider the system influenced by the external hyperbolic magnetic and Aharonov-Bohm (AB) forces. By using the Laplace transform method, the second-order differential equation of the Schrodinger equation is reduced to a first-order differential equation and so the eigenfunction and energy eigenvalues are obtained. The behavior of the bound state energy levels was demonstrated and analyzed using the computational method for various values of the potential parameter, mass parameter, external magnetic force, and AB force. Moreover, the thermomagnetic properties of the system were analyzed for H2, LiH, and HCl diatomic particles, involving the vibrational mean energy, vibrational free energy, vibrational entropy, specific heat capacity, magnetization, magnetic susceptibility, and persistent current.
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.
Abstract The influence of external magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules are investigated in this study. The two‐dimensional Schrödinger equation is solved with the Varshni‐screened Coulomb potential (VSCP) model using the well‐known Nikiforov‐Uvarov (NU) method. We obtained the energy eigenvalues and wavefunctions of the system and calculated the energy levels of some diatomic molecules in the m‐arbitrary state in the presence and absence of external magnetic and AB flux fields. The results show that combining the magnetic and AB flux fields eliminates degeneracy. We analyzed and plotted the partition function and other thermal properties in the presence of a magnetic field, an AB field, and a temperature‐dependent term.
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.
The hyperbolic Pöschl-Teller provides an analytically tractable model for studying bound states and represents an exactly solvable quantum system. However, the solvability of this system under the influence of an Aharonov-Bohm (AB) flux, and particularly for spin particles governed by the Pauli equation, remains largely unexplored within this framework. The present study bridges this gap by formulating and solving the Pauli equation for spin particles in cylindrical coordinates by applying a hyperbolic Pöschl-Teller potential with an Aharonov-Bohm flux field. Using the Hypergeometric method and variable separation, we derive the explicit quantization conditions that determine the energy spectrum. Key findings reveal spin-dependent energy shifts due to the interaction between the particle’s intrinsic magnetic moment and the AB flux field. Our work not only expands the study of analytically solvable quantum models but also highlights the intrinsic particle behavior arising from spin-field interactions in non-trivial geometries.
In this study, the influence of magnetic and Aharonov–Bohm (AB) flux fields on the magnetic properties of the Titanium Carbide (TiC) diatomic molecule at finite temperature is investigated. Using the generalized cosine Yukawa potential within the framework of the Nikiforov–Uvarov Functional Analysis (NUFA) method, the energy eigenvalue and the corresponding energy eigenfunction as well as the partition functions were obtained. Based on these, temperature-dependent magnetization, magnetic susceptibility, and persistent current were evaluated. The results show that magnetization increases with both magnetic field strength and AB flux, but decreases with temperature due to enhanced thermal agitation that disrupts magnetic dipole alignment. Similarly, magnetic susceptibility and persistent current diminish with temperature but exhibit higher magnitudes at stronger field intensities. These behaviors are consistent with Curie-like paramagnetism and agree with previous findings on related diatomic systems.