Killingbeck Potential Research Articles

Spin symmetry in the presence of a Killingbeck potential for a relativistic $$\Lambda$$-hypernuclei

In this work, we investigate the spin symmetry of a hypernuclei by focusing on the $$\Lambda$$ -hypernuclei. In this case, we solve the Dirac equation with scalar and vector Killingbeck potential and obtain energy eigenvalues and spinor wave functions for s-wave bound states by using the analytical method. Then, for some hypernuclei, their binding energy is reproduced. The results are in good agreement with corresponding experimental data.

Mass Spectrum of Mesons via the WKB Approximation Method

In this paper, we demonstrated that the multiple turning point problems within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation method can be reduced to two turning point one for a nonsymmetric potential function by using an appropriate Pekeris-type approximation scheme. We solved the Schrödinger equation with the Killingbeck potential plus an inversely quadratic potential (KPIQP) function. The special cases of the modeled potential are discussed. We obtained the energy eigenvalues and the mass spectra of the heavy QQ¯ and heavy-light Qq¯ mesons systems. The results in this present work are in good agreement with the results obtained by other analytical methods and available experimental data in the literature.

Position-dependent mass charged particles in magnetic and Aharonov–Bohm flux fields: separability, exact and conditionally exact solvability

Using cylindrical coordinates, we consider position-dependent mass (PDM) charged particles moving under the influence of magnetic, Aharonov–Bohm flux, and a pseudoharmonic or a generalized Killingbeck-type potential fields. We implement the PDM minimal coupling recipe (Mustafa in J Phys A Math Theor 52:148001, 2019), along with the PDM-momentum operator (Mustafa and Algadhi in Eur Phys J Plus 134:228, 2019), and report separability under radial cylindrical and azimuthal symmetrization settings. For the radial Schrödinger part, we transform it into a radial one-dimensional Schrödinger-type and use two PDM settings, $$g\left( \rho \right) =\eta \rho ^{2}$$ and $$g\left( \rho \right) =\eta /\rho ^{2}$$ , to report on the exact solvability of PDM charged particles moving in three fields: magnetic, Aharonov–Bohm flux, and pseudoharmonic potential fields. Next, we consider the radial Schrödinger part as is and use the biconfluent Heun differential forms for two PDM settings, $$g\left( \rho \right) =\lambda \rho $$ and $$g\left( \rho \right) =\lambda /\rho ^{2}$$ , to report on the conditionally exact solvability of our PDM charged particles moving in three fields: magnetic, Aharonov–Bohm flux, and generalized Killingbeck potential fields. Yet, we report the spectral signatures of the one-dimensional z-dependent Schrödinger part on the overall eigenvalues and eigenfunctions, for all examples, using two z-dependent potential models (infinite potential well and Morse-type potentials).

Study of the Dirac oscillator in the presence of vector and scalar potentials in the cosmic string space-time

In this paper, we use the functional Bethe ansatz method to solve the radial problem of the Dirac oscillator in cosmic string space-time, and its general solution under the Killingbeck potential plus isotonic oscillator potential in the limit of the spin and the pseudo-spin symmetries are further presented. Corresponding to the expressions of energies and wave function of bound state and first excited state are given. Furthermore, some particular cases including the Cornell potential, the Kratzer potential, the Killingbeck potential and the isotonic oscillator potentials are also addressed. It shows that the energy levels of the systems depend explicitly on the potential parameters [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the angular deficit parameter [Formula: see text] which characterize topological defect.

Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential

In this paper, we study the Schrödinger equation with non-central modified Killingbeck potential plus a ring-shaped-like potential problem, which is not spherically symmetric. The factorization method is used to solve the hypergeometric equation types which lead to solutions with the associate Laguerre function for the radial part and Jacobi polynomial for the polar part. We introduce the raising and lowering operators to calculate the energies eigenvalues, which show that the lack of spherical symmetry removes the degeneracy of second quantum number m which is completely expected. These obtained energies are better to explain the superposition of the energy levels of the atoms in the crystalline structure of molecules.

Non-degenerate γ-unstable Bohr Hamiltonian considering Killingbeck potential

In this paper, we want to study a generalized form of γ-unstable Bohr Hamiltonian in which there is no degeneracy between the excited levels. For this study, we consider a Killingbeck potential for the system. The results show the elimination of the degeneracy between the levels. According to the results we reproduce experimental data of some Xenon isotopes and discuss about them. The results show a good agreement between the theoretical prediction and experimental data.

Nuclear energy excitation by Bohr Hamiltonian for triaxial nuclei using Killingbeck plus Morse potential

This paper proposes an improved potential for the [Formula: see text]-part of the collective Bohr Hamiltonian, namely, a Killingbeck plus Morse potential, while the [Formula: see text]-part is solved for a triaxial deformation close to [Formula: see text]. The Asymptotic Iteration Method is used, involving the Pekeris approximation, to calculate the energy eigenvalues and the eigenfunctions after an exact separation of the Bohr Hamiltonian into its variables is achieved. The results of these calculations are applied for energy spectra of the low-lying states and for corresponding [Formula: see text] quadrupole transition probabilities of the [Formula: see text] isotopes. Moreover, the results of the present solution are compared with those of the well-known [Formula: see text] and [Formula: see text] models.

Perturbed Coulomb Potentials in the Klein–Gordon Equation: Quasi-Exact Solution

Using the Lie algebraic approach, we present the quasi-exact solutions of the relativistic Klein–Gordon equation for perturbed Coulomb potentials namely the Cornell potential, the Kratzer potential and the Killingbeck potential. We calculate the general exact expressions for the energies, corresponding wave functions and the allowed values of the parameters of the potential within the representation space of sl(2) Lie algebra. In addition, we show that the considered equations can be transformed into the Heun’s differential equations and then we reproduce the results using the associated special functions. Also, we study the special case of the Coulomb potential and show that in the non-relativistic limit, the solution of the Klein–Gordon equation converges to that of Schrodinger equation.

Investigation of Bohr Hamiltonian in presence of Killingbeck potential using bi-confluent Heun functions

In this study, Bohr Hamiltonian is studied for the triaxial and rotational cases. In both cases, Killingbeck potential is used as interaction. The wave function and energy of these cases are found using bi-confluent Heun functions. The results are examined by reproducing experimental data of some isotopes for each case. Energy levels of the isotopes are shown graphically as well as theoretical results for staggering in γ bands of the isotopes is discussed. In the next step, we argue about B(E2) transition rates of the isotopes for each case. The results have a good agreement with experimental data.

Investigation of the hybrid model with the Killingbeck potential in a variational approach

The energy spectrum and transition rates have been obtained for some nuclei in critical point by employing the hybrid collective model. For this purpose, the corresponding Hamiltonian with β-dependent Killingbeck potential has been solved by the variational method. Our results have been compared with other references and experimental data.

A New Approach for Obtaining the Non-Strange Baryons Spectrum in a Phenomenological Interaction Potential

In our work, we present the nonrelativistic quark model and a new mass formula for study the non-strange baryons octet and decuplet masses. Our model contains a dominant SU(6)-invariant part accounting for the average multiplet energies, and a perturbative SU(6)-violating interaction for the splitting within the multiplets, a structure which is inspired by early Lattice QCD calculations. For our purpose we introduced a spin independent description for SU(6) invariant part of the spectrum, we presented the analytical solution of three particle Schrodinger equation under the suitable phenomenological interaction potential by using the anzast method, through which the average energy values of the nonstrange resonances are reproduced. To describe the hyperfine structure of the baryon and splittings within the SU(6)-multiplets, we used the generalized Gursey Radicati mass formula. A comparison between our calculations and the experimental data shows that the spectrum of the Roper resonances, the ground states and the excited multiplets up to three GeV are in general well reproduced and comparable with the experimental spectrum. Also one can conclude that; the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.

Investigation of Conformable Fractional Schrödinger Equation in Presence of Killingbeck and Hyperbolic Potentials**Supported by the National Research Foundation of Korea Grant Funded by the Korean Government under Grant No. NRF-2015R1D1A1A01057792

In this article, conformable fractional form of Schrödinger equation has been presented. Then in this formalism two different and well-known potential have been come in. Wave function of these potential are obtained in terms of Heun function and energy eigen values of each case is determined as well.

The Determination of the Spectrum Energy on the model of DNA-protein interactions using WKB approximation method

The spectrum energy’s equation for Killingback potential on the model of DNA and protein interactions was obtained using WKB approximation method. The Killingbeck potential was substituted into the general equation of WKB approximation method to determine the energy. The general equation required the value of critical turning point to complete the form equation. In this research, the general form of Killingbeck potential was causing the equation of critical turning point turn into cube equation. In this case we take the value of critical turning point only with the real value. In mathematical condition, it was satisfied with requirement Discriminant was less than or equal to 0. If D=0, it would give two values of critical turning point and if D<0, it would give three values of critical turning point. In this research we present both of those requirements to complete the general Equation of Energy.

A model of a nonlinear DNA-protein interaction system with Killingbeck potential and its stability

In this paper, we presented a model of a nonlinear DNA-protein interaction system. The interaction system consisted of a molecule of protein bound with a single chain of DNA. The interaction between DNA chain, especially adenine and thymine, and DNA-protein bound to glutamine and adenine. The forms of these bonds are adapted from the hydrogen bonds. The Killingbeack potential were used to describe both of the interactions. We proposed the Hamiltonian equation to describe the general model of interaction. The interaction model is satisfied when a protein molecule triggers pulses on a DNA chain. An initial shift in position of protein xm should trigger the shift in position of DNA ym, or alter the state. However, an initial shift in DNA, yn, should not alter the state of a rest protein (i.e. xm = 0), otherwise, the protein would not steadily bind. We also investigated the stability of the model from the DNA-protein interaction with Lyapunov function. The stability of system can be determined when we obtained the equilibrium point.

Supersymmetric approach for Killingbeck radial potential plus noncentral potential in Schrodinger equation

Killingbeck radial potential, which consists of harmonic oscillator, linier and Coulomb potentials, is combined with non-central potential. The solution of three dimensional Schrodinger equation for Killingbeck potential is combined with Poschl-Teller potential and Symmetrical Top non-central potentials are investigated using supersymmetry (SUSY) operator. The non-relativistic energy is obtained which is infuenced by potentials and the wave functions are produced by using SUSY operator.

Nonrelativistic Shannon information entropy for Killingbeck potential

The Shannon entropy of a nonrelativistic quantum system is investigated with the Killingbeck potential, which includes Coulomb, linear, and harmonic terms. The position and momentum information entropies for the low-lying states n = 0, 1 are calculated. Some interesting features of the information entropy densities as well as the probability densities are demonstrated. The Bialynicki-Birula–Mycielski inequality is checked regarding the results.

Study of Davydov–Chaban approach considering shifted Killingbeck potential for any l-state

In this paper, Davydov–Chaban approach to study collective motion of atomic nuclei has been mentioned in detail. First by considering a shifted Killingbeck potential, we obtain the wave function of such system by taking an ansatz method. Then we consider a special case of shifted Killingbeck potential to recover known results.

A New Method for Obtaining the Baryons Mass under the Killingbeck Plus Isotonic Oscillator Potentials

The spectrum of ground state and excited baryons (N, Δ, Λ, Σ,Ξ, and Ω particles) has been investigated by using nonrelativistic quantum mechanics under the Killingbeck plus isotonic oscillator potentials. Using the Jacobi coordinates, anzast method, and generalized Gürsey Radicati (GR) mass formula the three-body-wave equation is solved to calculate the different states of the considered baryons. A comparison between our calculations and the available experimental data shows that the position of the Roper resonances of the nucleon, the ground states, and the excited multiplets up to three GeV are in general well reproduced. Also one can conclude that the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.

Exactly separable Bohr Hamiltonian with the Killingbeck potential for triaxial nuclei

After pioneering work by Bohr, Mottelson and their numerous colleagues, the essential framework for understanding collective model is introduced. One of the applications of this framework is the study of shape phase transition, vibrational and rotational energy spectrum of nuclei. We consider the Bohr Hamiltonian and solve the beta and gamma part equation of it, by considering that reduced potential and wave function are exactly separable. In the beta part equation we consider the Killingbeck potential and derive the wave function and energy spectrum of it.

Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

Algebraic solutions of the D-dimensional Schrödinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl(2) algebraization.