Wave Function Ansatz Method Research Articles

The influence of magnetic and Aharanov–Bohm fields on energy spectra of diatomic molecules in the framework of the Dirac equation with the generalized interaction potential

AbstractIn this study, we present the relativistic and non‐relativistic solutions of the Dirac equation with the spin symmetry for the generalized Cornell potential (GCP) using the wave function ansatz method in the existence of external magnetic and Aharanov–Bohm (AB) flux fields. The relativistic energy eigenvalues and the corresponding eigenfunctions are found for varied vibrational and magnetic quantum numbers. By adapting the GCP parameters, we derive the relativistic and non‐relativistic energy eigenvalues with and without external fields for a set of potential models including the Killingbeck, harmonic oscillator, pseudoharmonic, anharmonic, Cornell, Coulomb, Kratzer, and modified Kratzer potentials. Additionally, the non‐relativistic energy spectra of the Kratzer and modified Kratzer potentials are reported with and without external magnetic and AB flux fields for several diatomic molecules (DMs). We discovered that in the existence of external magnetic and AB flux fields, the non‐relativistic energy spectrum increases and degeneracy disappears. Furthermore, the AB flux field has a stronger impact on the energy spectrum than the magnetic field. To substantiate our findings, we calculate the energy levels of the Kratzer and modified Kratzer potentials for diverse DMs and find that they are perfectly consistent with previous studies.

The Solutions of the D-dimensional Schrodinger Equation for the Potential V(r) = ar-6+br-5+cr-4+dr-3+er-2+fr-1

The solutions of the D-dimensional Schrodinger equation was solved by using Wavefunction Ansatz method. We used the form of potential as V(r) = ar-6+br-5+cr-4+dr-3+ er-2+fr-1. The D-dimensional Schrodinger equation was separated to radial part and angular part. The radial part of D-dimensional Schrodinger equation solved using Wavefunction Ansatz method. We obtained the energy equation and the radial wavefunctions.

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

Abstract The Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

Nonrelativistic molecular models under external magnetic and AB flux fields

By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary m-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We calculate the energy levels of some diatomic molecules in the presence and absence of external magnetic and AB flux fields using different potential models. We found that the effect of the Aharonov–Bohm field is much as it creates a wider shift for m≠0 and its influence on m=0 states is found to be greater than that of the magnetic field. To show the accuracy of the present model, a comparison is made with those ones obtained in the absence of external fields. An extension to 3-dimensional quantum system have also been presented.

INFLUENCE OF EXTERNAL FIELDS ON THE KILLINGBECK POTENTIAL: QUASI EXACT SOLUTION

The Killingbeck potential consists of oscillator potential plus Cornell potential, i.e. ar2+ br - c/r, that it has received a great deal of attention in particle physics. In this paper, we study the energy levels and wave function for arbitrary m-state in two-dimensional (2D) Schrödinger equation (SE) with a Killingbeck potential under the influence of strong external uniform magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the Schrödinger equation with Killingbeck potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.

Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields

The Klein-Gordon (KG) equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB) flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL= 0) and AB flux field (ξ=0) cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.

Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

Relativistic Bound States of Spinless Particle by the Cornell Potential Model in External Fields

The two-dimensional (2D) relativistic bound states of a spinless particle placed in scalarS(r)and vectorV(r)Cornell potentials (withS(r)>V(r)) are obtained under the influence of external magnetic and Aharonov-Bohm (AB) flux fields using the wave function ansatz method. The relativistic energy eigenvalues and wave functions are found for any arbitrary state with principalnand magneticmquantum numbers. Further, we obtain the eigensolutions in any dimensional spaceDwithout external fields. We also find the relativistic and nonrelativistic bound states for Coulomb, harmonic oscillator, and Kratzer potentials.

Relativistic effect of external magnetic and Aharonov-Bohm fields on the unequal scalar and vector Cornell model

The Cornellpotential consists of linear and Coulomb potentials, i.e. −a/r+br, and has attracted a great deal of attention in particle physics. In this article, we study the energy levels and the wave function for an arbitrary m-state in the two-dimensional (2D) Klein-Gordon (KG) equation with the unequal scalar-vector Cornell potentials under the influence of strong external uniform magnetic and Aharonov-Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the KG equation with the Cornell potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.

A new method for obtaining the spectrum of baryon resonances in the Killingbeck potential

In this paper, we investigate the spin- and flavor-dependent SU(6) violations in the baryon resonances spectrum using a simple approach based on the Gürsey–Radicati (GR) mass formula. The relativistic energy spectrum has some very important features that makes it vastly superior to the nonrelativistic one; so, in order to obtain the average energy value of each SU(6) multiplet, we have exactly solved the Dirac equation for the Killingbeck potential analytically by using the wave function ansatz method. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula for the description of the spectrum) show that the strange and nonstrange baryon spectra are, in general, fairly well reproduced. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets with more than 2 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon. Finally, we compare the results obtained by the Dirac equation for the Killingbeck potential with the corresponding results of the Schrödinger equation for the Cornell potential and we find that our model has improved the results of the nonrelativistic model.

Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit

The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.