Thermodynamic properties of Aharonov-Bohm (AB) and magnetic fields with screened Kratzer potential

In this study, the Schrodinger equation (SE) with screened Kratzer potential (SKP) in the presence of external magnetic and AB-flux fields is investigated using the factorization method. The eigenvalue and eigenfunction for the system are obtained in closed form. It is found that the present of the magnetic field partially removes the degeneracy when the screening parameter of the potential was small but the addition of the AB field removed the degeneracy faster and better. The magnetization and magnetic susceptibility of the system are evaluated at zero and finite temperatures and other thermodynamic properties of the system are discussed. More so, the presence of the AB-flux field makes the system to exhibit a both a paramagnetic and diamagnetic behavior. A straight forward extension of these results to three dimension shows that the present result is consistent with those obtained in literature.Comment: 30 pages, 9 figures. arXiv admin note: text overlap with arXiv:1911.0199

Exact solutions of κ-dependent Schrödinger equation with quantum pseudo-harmonic oscillator and its applications for the thermodynamic properties in normal and superstatistics

The effects of the curvature parameters on the energy eigenvalues and thermodynamic properties of quantum pseudoharmonic oscillator are investigated within the framework of nonrelativistic quantum mechanics. By employing Nikiforov-Uvarov method, the energy spectra are obtained and used to study the ordinary statistics and q-deformed superstatistics as a function of temperature in the presence and absence of the curvature parameters. It is shown that the q-deformed supertatistics properties of the quantum pseudoharmonic oscillator reduce to the ordinary statistical properties in the absence of the deformation parameter. Finally, our results are illustrated graphically to show the behaviour of the energy spectra and thermodynamic properties for the three curvature parameters:κ=−1,κ=1andκ=0

The statistical properties of the Varshni potential model using modified factorization method

We have solved the Schrodinger equation with Varshni potential model using the modified factorization method. By employing the Greene Aldrich approximation scheme and an appropriate transformation scheme, analytical expressions of the energy eigenvalues and its corresponding normalized eigenfunctions were obtained in terms of the hypergeometric function in closed form. Numerical results of the energy eigenvalues for different quantum states were computed at varying screening parameters and discussed. The effects of the Varshni potential model parameters on the energy eigenvalues have been evaluated. The analytical expression of the energy eigenvalues obtained have been used to obtain an expression for the ro-vibrational partition function and other thermodynamic functions for the Varshni potential model. The variation of the thermodynamic functions with temperature for different quantum states have been analyzed. Our results obtained promises to be relevant in different areas of studies including molecular and chemical physics. Keywords: Varshni Potential, Modified factorization method, Energy eigenvalues, Partition function, Thermodynamic properties

Solutions of the Klein Gordon equation with generalized hyperbolic potential in D-dimensions

We solve the D- dimensional Klein-Gordon equation with a newly proposed generalized hyperbolic potential model, under the condition of equal scalar and vector potentials. The relativistic bound state energy equation has been obtained via the functional analysis method. We obtained the relativistic and non-relativistic ro-vibrational energy spectra for different diatomic molecules. The numerical results for these diatomic molecules tend to portray inter-dimensional degeneracy symmetry. Variations of the energy eigenvalues obtained with the potential parameters have been demonstrated graphically. Our studies will find relevant applications in the areas of chemical physics and high-energy physics

Bound and scattering states solutions of the Klein–Gordon equation with generalized Mobius square potential in D-dimensions

In this study, the Klein–Gordon equation (KGE) was solved with the generalized Mobius square (GMS) potential using the functional analysis approach (FAA) in D-dimensions. By employing the Pekeris-type approximation scheme, the relativistic and nonrelativistic bound state energies were obtained in closed form. Also, the expression for the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of nitrogen monoiodide (NI) diatomic molecule were studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule. Hence, this concept is applicable in the areas of chemical physics, nuclear and particle physics. Graphic abstract: In this study, the relativistic and nonrelativistic bound state energies of KGE with the GMS potential were obtained in D-dimensions using the FAA. In addition, the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of NI diatomic molecule were studied. The inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule was obtained at unique quantum states

Energy spectra and magnetic properties of diatomic molecules in the presence of magnetic and AB fields with the inversely quadratic Yukawa potential

Within the framework of non-relativistic quantum mechanics, the inversely quadratic Yukawa potential is investigated in the presence of external magnetic and Aharonov–Bohm (AB) fields. The Schrödinger equation is solved via the Nikiforov–Uvarov functional analysis (NUFA) method, and the obtained energy eigenvalues are discussed. It is shown that the presence of the magnetic and AB fields removes the degeneracy. The partition function of the system and the thermodynamic properties of the system such as Helmholtz free energy, entropy, internal energy, specific heat and the magnetization and magnetic susceptibility of the system are calculated in detail. The magnetic properties of the QYP in the presence of the magnetic and AB fields are also discussed

Thermodynamic properties of Aharanov–Bohm (AB) and magnetic fields with screened Kratzer potential

In this study, the Schrödinger equation (SE) with screened Kratzer potential (SKP) in the presence of external magnetic and AB-flux fields is investigated using the factorization method. The eigenvalue and eigenfunction for the system are obtained in closed form. It is found that the presence of the magnetic field partially removes the degeneracy when the screening parameter of the potential was small (α = 0.005) but the addition of the AB field removed the degeneracy faster and better. The magnetization and magnetic susceptibility of the system are evaluated at zero and finite temperatures and other thermodynamic properties of the system are discussed. More so, the presence of the AB-flux field makes the system to exhibit a both a paramagnetic and diamagnetic behavior. A straight forward extension of these results to three dimension shows that the present result is consistent with those obtained in literature