Bound State Energy Spectrum Research Articles

Investigation of bound state energy spectra for fermionic particles in the presence of ultra generalized exponential hyperbolic potential model

By considering the ultra generalized exponential hyperbolic potential, which covers many potential types, the solutions of the Dirac equation with spin/pseudo-spin symmetric limits are achieved. In both approaches, the relation giving the bound state energy eigenvalues is obtained in a closed form. By using these relations, the energy values are calculated numerically for both symmetry cases via the software program. In addition, it has been identified how the bound state energy eigenvalues depend on the parameters. Besides, the energy equations for the Schrödinger and Klein–Gordon particles in the limit states are derived.

Andreev bound states in Josephson junctions of semi-Dirac semimetals

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor–barrier–superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum ɛ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of ɛ on the superconducting phase difference ϕ, we compute the variation of Josephson current as a function of ϕ.

Nonrelativistic bound-state energy spectrum and persistent current in the modified Rosen–Morse oscillator confined to a 2D electromagnetic potential field

Nonrelativistic bound-state energy spectrum and persistent current in the modified Rosen–Morse oscillator confined to a 2D electromagnetic potential field

Bound-state energy spectrum and thermochemical functions of the deformed Schiöberg oscillator

In this study, a diatomic molecule interacting potential such as the deformed Schiöberg oscillator (DSO) have been applied to diatomic systems. By solving the Schrödinger equation with the DSO, analytical equations for energy eigenvalues, molar entropy, molar enthalpy, molar Gibbs free energy and constant pressure molar heat capacity are obtained. The obtained equations were used to analyze the physical properties of diatomic molecules. With the aid of the DSO, the percentage average absolute deviation (PAAD) of computed data from the experimental data of the 7Li2 (2 3Πg), NaBr (X 1Σ+), KBr (X 1Σ+) and KRb (B 1Π) molecules are 1.3319%, 0.2108%, 0.2359% and 0.8841%, respectively. The PAAD values obtained by employing the equations of molar entropy, scaled molar enthalpy, scaled molar Gibbs free energy and isobaric molar heat capacity are 1.2919%, 1.5639%, 1.5957% and 2.4041%, respectively, from the experimental data of the KBr (X 1Σ+) molecule. The results for the potential energies, bound-state energy spectra, and thermodynamic functions are in good agreement with the literature on diatomic molecules.

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

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 H2, 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.

Effects of Yukawa confining potential on Klein-Gordon oscillator

In this paper, we study the quantum dynamics of relativistic Klein-Gordon oscillator with Yukawa confining potential. We obtain approximate bound state energy spectrum and the corresponding wave function expressed in terms of biconfluent Hun function using the extended Nikiforov-Uvarov method. The effects of the screening parameter on the energy spectrum of the Klein-Gordon oscillator are discussed in details.

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at finite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.

Thermal and atomic properties of hydrogen atom and diatomic molecules in Wilson-Racah Quantum System

In this study, a conventional quantum mechanics in which the potential function is not specified but replaced by specifying four parameters Wilson-Racah orthogonal polynomials in the energy and physical parameter space was presented. The wave function is written as a bounded sum of elements of a complete basis with these polynomials as expansion coefficients. By finding the asymptotic of these Wilson – Racah polynomials, the physical properties of the corresponding system (wave function, bound state energy spectrum and/or scattering phase shift) was obtained. Wilson – Racah quantum system was applied to determine the thermodynamics and atomic properties of Hydrogen atom and diatomic molecules. All properties of associated physical systems are obtained directly and simply from the asymptotic of the associated orthogonal polynomials. This new model, gives good an approximate prediction of the Hydrogen atom energy with an estimated average error of 0.125%. The proposed procedure merely relies on experimental values of five molecular constants. The average relative percentage deviations of the thermodynamic properties’ functions Q, U, C, S and F which are 2.42, 0.45, 0.30, 1.23 and 1.50% satisfied the experimental finding as ascertained. These represent satisfactory compromise between accuracy and rapid computations.

Bound and scattering states of the Klein-Gordon equation for shifted Tietz-Wei potential with applications to diatomic molecules

In this study, the Klein-Gordon equation (KGE) was solved with the shifted Tietz-Wei potential using the Nikiforov-Uvarov-functional-analysis (NUFA) in higher dimensions. By employing the improved approximation scheme, the relativistic energy spectra of the shifted Tietz-Wei potential was obtained in closed form. In addition, the scattering state phase shift expression for the shifted Tietz-Wei potential was obtained in higher dimensions. The effects of the vibrational and rotational quantum numbers on the bound state energy spectra and scattering phase shift of chlorine dimer, and iodine monochloride, diatomic molecules were studied numerically and graphically at different dimensions. Interestingly, there exists inter-dimensional degeneracy symmetry for the bound state and scattering phase shift of the diatomic molecular systems considered. Our results were generally in good agreement with those obtained in literatures.

The solution of D+1-dimensional Dirac equation for diatomic molecules with the Morse potential

In this paper, the solutions of the D+1-dimensional Dirac equation in the presence of the Morse potential are investigated by using the supersymmetric quantum mechanics and shape invariance theory with spin symmetry. The bound state energy spectrum and the ground state wave function are calculated by supersymmetry approach. Also, it is shown that the energy spectrum and vibrational energy eigenvalue at the critical point can be obtained by a numerical method which is called the asymptotic iteration method. The $$X^2\Sigma ^+$$ state of the CP and $$X^1\Sigma ^+$$ state of the $$SiF^+$$ molecules are considered, and their relativistic energy eigenvalues are studied.

Effects of extended uncertainty principle on the relativistic Coulomb potential

The relativistic bound-state energy spectrum and the wave functions for the Coulomb potential are studied for de Sitter and anti-de Sitter spaces in the context of the extended uncertainty principle. Klein–Gordon and Dirac equations are solved analytically to obtain the results. The electron energies of hydrogen-like atoms are studied numerically.

Mass spectrum of heavy quarkonium for screened Kratzer potential (SKP) using series expansion method

In this study, the radial Schrodinger equation is solved with the screened Kratzer potential using the series expansion method. The bound state energy spectra are obtained. To check the correctness of the result obtained from this method, we carry out suitable adjustments to the screened Kratzer potential parameters resulting in potential models, such as the Kratzer and Coulomb potentials are deduced as special cases. The numerical values of the energy spectra of the special cases (Kratzer potential) for hydrogen chloride and lithium hydride diatomic molecules are computed for different quantum numbers; n and l and the results are in consonance with the theoretical works of similar investigation. The expression for the energy spectra is applied to obtain the mass spectra of heavy quarkonium systems (charmonium and bottomonium). The numerical results agree with the experimental values and theoretical studies in previous works. Our results will have possible applications in high energy physics, molecular physics, etc.

Bound State Solution of Radial Schrodinger Equation for the Quark–Antiquark Interaction Potential

This work analytically solved the radial Schrodinger equation with an exponential, generalised, anharmonic Cornell potential using the series expansion method. It also obtained the bound state energy spectra. Through suitable adjustments to the potential parameters, the well-known potential models, such as the pseudoharmonic and Kratzer potentials, were deduced. With the potential parameters also adjusted, the energy spectra for the pseudoharmonic and Kratzer potentials were obtained as special cases. The numerical values of the energy spectra for CO, NO, CH and N2 diatomic molecules were computed for different quantum numbers, n and l, respectively. In addition, with the application of the spectra, an expression for the mass spectra of heavy quarkonium systems (charmonium and bottomonium) was obtained. The results agree with the experimental and theoretical studies in previous works.

Scattering description of Andreev molecules

An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.

Bound states and the potential parameter spectrum

In this article, we answer the following question: If the wave equation possesses bound states, but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated wavefunctions)? To answer this question, we use the “tridiagonal representation approach” to solve the wave equation at the given energy by expanding the wavefunction in a series of energy-dependent square integrable basis functions in configuration space. The expansion coefficients satisfy a three-term recursion relation, which is solved in terms of orthogonal polynomials. Depending on the selected energy, we show that one of the potential parameters must assume a value from within a discrete set called the “potential parameter spectrum” (PPS). This discrete set is obtained from the spectrum of the above polynomials and can be either a finite or an infinite set. Inverting the relation between the energy and the PPS gives the bound state energy spectrum. Therefore, the answer to the above question is affirmative.

Effects of Generalized Uncertainty Principle on the $$\mathbf (1+1) $$ Dimensional DKP Oscillator with Linear Potential

Based on $$ 3\times 3$$ irreducible representation of Duffin–Kemmer–Petiau (DKP) algebras, we obtain the bound-states energy spectrum, the wave function and the probability density of DKP oscillator with linear potential under the effect of Generalized Uncertainty Principle in the momentum space representation. In addition, the numerical results of the bound-states energy spectrum are discussed. It shows that the deformation parameter $$\beta $$ and the linear potential parameter $$\lambda $$ have non-negligible effect on the $$(1 + 1)$$ dimensional DKP oscillator system.

Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

In this paper, we obtained the exact bound state energy spectrum of the Schrödinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.

Supersymmetry approach to the Dirac equation in the presence of the deformed Woods-Saxon potential

In this paper, by using the supersymmetric quantum mechanics and shape invariance theory, the Dirac equation is studied with spin symmetry for the deformed Woods-Saxon potential. The bound state energy spectrum and the corresponding spinor wave functions are calculated by supersymmetry approach.

Bound states of Newton’s equivalent finite square well

In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.

An investigation of the bound-state solutions of the Klein-Gordon equation for the generalized Woods-Saxon potential in spin symmetry and pseudo-spin symmetry limits

Recently, scattering of a Klein-Gordon particle in the presence of mixed scalar-vector generalized symmetric Woods-Saxon potential was investigated for the spin symmetric and the pseudo-spin symmetric limits in one spatial dimension. In this manuscript, the bound state solutions of the Klein-Gordon equation with mixed scalar-vector generalized symmetric Woods-Saxon potential are examined analytically within the framework of spin and pseudo-spin symmetry limits. We prove that the occurrence of bound state energy spectrum exists only in the spin symmetric limit, while in the pseudo-spin symmetric limit, the bound state spectrum does not exist. Besides the theoretical proof, the Newton-Raphson numerical methods are used to calculate the bound state energy spectra of a neutral Kaon particle, confined in a generalized symmetric Woods-Saxon potential, energy well constituted with repulsive or attractive surface interactions, for the spin and pseudo-spin symmetric limits, respectively. Numerical results are consistent with the non-existence of the bound state energy spectrum in the pseudo-spin symmetric limit.