Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg–Horodecki equation

We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schr¨odinger equation,the Feinberg–Horodecki equation,with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials.The present work is illustrated with two special cases of the general form:the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.

Spin and pseudospin symmetric Dirac particles in the field of Tietz-Hua potential including Coulomb tensor interaction

Approximate analytical solutions of the Dirac equation for Tietz-Hua （TH） potential including Coulomb-like tensor （CLT） potential with arbitrary spin-orbit quantum number K are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms K（K± 1）r^-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov-Uvarov （NU） method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

The decoherence of the triangular and Coulomb bound potential quantum dot qubit

We study the eigenenergies and eigenfunctions of the ground and first-excited states of an electron which is strongly coupled to an LO-phonon in a quantum dot with a triangular bound potential and Coulomb bound potential by using the Pekar variational method. This system may be used as a two-level qnbit. Phonon spontaneous emission causes the decoherence of the qubit. Numerical calculations are performed on the decoherence rate as a function of the polar angle, the Coulomb binding parameter, the coupling strength, the confinement length of the quantum dot and the dispersion coefficient.

Exact solutions of the Dirac equation with Pschl-Teller double-ring-shaped Coulomb potential via the Nikiforov-Uvarov method

Exact analytical solutions of the Dirac equation are reported for the Poschl-Teller double-ring-shaped Coulomb potential.The radial,polar,and azimuthal parts of the Dirac equation are solved using the Nikiforov-Uvarov method,and the exact bound-state energy eigenvalues and corresponding two-component spinor wavefunctions are reported.

Introduction of the Coulomb dressed potential into atomic scattering

The model of the Coulomb dressed potential is applied to solving the problem of electron scattering for simplifying the calculation in the electrostatic field and the excimer laser field. The introduction and the application of the model are based on the electric dipole approximation, so the contribution of the electric multipole is neglected. In this paper, rigorous analysis and deduction are carried out for the introduction of the dressed Coulomb potential into the laser field. It is found that the introduction of the dressed potential in the fractional form is feasible only when the laser field （not including far ultraviolet field and x-ray） is a weak field, i.e. the quiver radius of the free electron is smaller than the atomic scale. In addition, the necessary analysis is also conducted of the limitation of the application of the Coulomb dressed potential.

Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential

Poschl-Teller double-ring-shaped Coulomb （PTDRSC） potential, the Coulomb potential surrounded by PSschl- Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ,θ and τ coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schr6dinger equation with PTDRSC potential are presented. The normalized φ,θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.

Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential

In this work, we modeled and simulated the electric potential generated by point charges in the region of grounded conductor planes for Yukawa potential (e−μ/r) and Coulomb potential (1/r). We show the symbolic expression for the electric potential and some graphs for it and for the electric field with different values of μ. We observe that the electric potential decreases as the value of μ increases and that does not allow all the charge to be distributed on the surface of the conductor.

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.

Point Charge between Two Grounded and Conducting Planes Forming a 60°Angle and for Yukawa’s Potential and Coulomb’s Potential

For a point charge between two grounded conductor planes forming a 60° angle, the potential and electric field generated by point charge for Yukawa’s potential (e-μr/r) and Coulomb’s potential (1/r) are modeled and simulated. The expression for the potential that generalizes the cases discussed in López-Mariño, M. and Trujillo Caballero, J. (2017) Point Charges and Conducting Planes for Yukawa’s Potential and Coulomb’s Potential. Journal of Electromagnetic Analysis and Applications, 9, 135-146. https://doi.org/10.4236/jemaa.2017.910012 is presented. Graphs for the potential and electric field for both cases are showed using Maple, that of Coulomb and that of Yukawa for different values of μ . The purpose of this work is to offer students a practical guide for problem analysis of electrostatics using Maple’s capabilities as a computational tool.

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm （AB） flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.

Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot,we obtain theeigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method ofPekar type.This system in a quantum dot may be employed as a two-level quantum system-qubit.When the electronis in the superposition state of the ground state and the first-excited state,we obtain the time evolution of the electrondensity.The relations of the probability density of electron on the temperature and the electron-LO-phonon couplingconstant and the relations of the period of oscillation on the temperature,the electron-LO-phonon coupling constant,the Coulomb binding parameter and the confinement length are derived.The results show that the probability densityof electron oscillates with a period when the electron is in the superposition state of the ground and the first-excitedstate,and show that there are different laws that the probability density of electron and the period of oscillation changewith the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher.Andit is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases withincreasing the confinement length not only at lower temperatures but also at higher temperatures.

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

Relativistic Scattering States of Coulomb Potential Plus a New Ring-Shaped Potential

In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/27π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.

Inverse Spectral Theory for a Singular Sturm Liouville Operator with Coulomb Potential

We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.

A New Method for the Atomic Ground-State Energy in the Screened Coulomb Potential

The new method proposed recently by Friedberg,Lee and Zhao is applied to the derivation of the atomic ground-state energy with the inclusion of the screening effect.The present results are compared with those obtained in the pure Coulomb potential and by the variational approach.The overall good results are obtained with this new method.

Momentum Eigensolutions of Feinberg-Horodecki Equation with Time-Dependent Screened Kratzer-Hellmann Potential

We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.

p-wave resonances in the exponential cosine screened Coulomb potential

We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.

Separation of Variable Treatment for Solving Time—Dependent Potentials

We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.

A Robust Numerical Method for Generalized Coulomb and Self-Polarization Potentials of Dielectric Spheroids

By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium,a robust numerical method for calculating the generalized Coulomb and self-polarization potentials of the dielectric spheroid is presented in this paper.The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest step-like model of the dielectric interface,but also completely eliminate the potential numerical divergence which may occur in other treatments.Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a general three-layer dielectric model goes to infinity.