Bound state solutions of the Dirac equation with the Deng–Fan potential including a Coulomb tensor interaction

Approximate analytical solutions of the Dirac equation in the case of pseudospin and spin symmetry limits are inves- tigated under the Deng-Fan potential by applying the asymptotic iteration method for the arbitrary quantum numbers n and ~~. Some of the numerical results are also represented in both pseudospin symmetry and spin symmetry limits.     

Spin symmetric solutions of Dirac equation with PSschl-Teller potential

The approximate analytical solutions of the Dirac equation with the Poeschl-Teller potential is presented for arbitrary spin-orbit quantum number κ within the framework of the spin symmetry concept. The energy eigenvalues and the corresponding two Dirac spinors are obtained approximately in closed forms. The limiting cases of the energy eigenvalues and the two Dirac spinors are briefly discussed.     

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 κ are obtained within the Pekeris approximation scheme to deal with the spin-orbit coupling terms κ(κ± 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.     

Relativistic symmetries of Deng Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.     

Pseudospin symmetry of the Dirac equation for a MSbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.     

Stable solutions for qq^- bound states with a regularized Breit potential

The Breit interaction contains singular terms which may lead to an instability in quark-antiquark bound state calculations. We regularize the Breit interaction by multiplying the singular terms in momentum space by the form factor μ^2/（q^2＋μ^2） such that the interaction is not singular at the origin and the intermediate-and long-range parts of the interaction remain unchanged. The singular terms in the Breit potential find their stable contributions in the calculations after being multiplied by the form factor with different powers. Such a regularized Breit potential with a linear and a relativistically corrected confining potential are applied to the study of qq^- bound states. The spectra for most familiar mesons are consistently obtained and agree well with the experimental data.     

Approximate solutions of SchrSdinger equation for Eckart potential with centrifugal term

The approximate analytical solutions of the Schrodinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ= λ=1, and β=0, are investigated.     

Relativistic symmetries in the Hulth6n scalar-vector-tensor interactions

In the presence of spin and pseudospin （p-spin） symmetries, the approximate analytical bound states of the Dirac equation for scalar-vector-tensor Hulth6n potentials are obtained with any arbitrary spin-orbit coupling number using the Pekeris approximation. The Hulth6n tensor interaction is studied instead of the commonly used Coulomb or linear terms. The generalized parametric Nikiforov-Uvarov （NU） method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. It is shown that tensor interaction removes degeneracy between spin and p-spin doublets. Some numerical results are also given.     

Meson spectra governed by the Fermi-Breit potential

We calculate the meson mass spectra in a quark potential model by using the complete Fermi-Breit potential including the terms of orbit-orbit interaction, spin-orbit coupling, and tensor force interaction. We find that these terms give nontrivial contributions to the calculated meson spectra. The orbit-orbit coupling term may lead to an instability of the solution of the Schr5dinger equation and should be regularized.     

Solution of Klein-Gordon Equation for Pseudo-Coulomb Potential Plus a New Ring-Shaped Potential

Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of the Klein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously, energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions are expressed by confluent hypergeogetric and hypergeogetric functions respectively.     

Supersymmetry and Solution of Dirac Equation with Vector and Scalar Potentials

The Dirac equations with vector and scalar potentials of the Coulomb types in two and three dimensions are solved using the supersymmetric quantum mechanics method. For the system of such potentials, the analytical expressions of the matrix dements for both position and momentum operators are obtained.     

Localization and recurrence of a quantum walk in a periodic potential on a line

We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.     

Bound states of the SchrSdinger equation for the PSschl-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.     

Exact solution of Schrdinger equation with q-deformed quantum potentials using Nikiforov–Uvarov method

In this paper,we present the exact solution of the one-dimensional Schrdinger equation for the q-deformed quantum potentials via the Nikiforov–Uvarov method.The eigenvalues and eigenfunctions of these potentials are obtained via this method.The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed.The PT-symmetry and Hermiticity for these potentials are also discussed.     

A higher-dimensional model of the nucleon-nucleon central potential

Based on a theory of extra dimensional confinement of quantum particles [E. R. Hedin, Physics Essays, 2012, 25（2）： 177], a simple model of a nucleon nucleon （NN） central potential is derived which quantitatively reproduces tile radial profile of other models, without adjusting any free pa- rameters. It is postulated that a higher-dimensional simple harmonic oscillator confining potential localizes particles into three-dimensional （3D） space, but allows for an ewmescent penetration of the particles into two higtmr spatial dimensions. Producing an effect identical with the relativistic quan- tum phenolnenon of zitterbewegung, the higher-dimensional oscillations of amplitude h（mc） call be alternatively viewed as a localized curvature of 3D space back and forth into the higher dimensions. The overall spatial curvature is proportional to the particle＇s extra-dimensional ground state wave function in tile higher-dimensional harmonic confining potential well. Minimizing the overlapping curvature （proportional to the energy） of two particles in proximity to each other, subject to the constraint that for the two particles to occupy the same spatial location one of them must be excited into the 1st excited state of the harmonic potential well, gives the desired NN potential. Specifying only the imcleon masses, the resulting potential well and repulsive core reproduces the radial profile of several published NN central potential models. In addition, the predicted height of the repulsive core, when used to estimate the maximum neutron star mass, matches well with the best estimates from relativistic theory incorporating standard nuclear matter equations of state. Nucleon spin, Coulomb interactions, and internal nucleon structure are not considered in the theory as presented in this article.     

A two-dimensional fully analytical model with polarization effect for off-state channel potential and electric field distributions of GaN-based field-plated high electron mobility transistor

In this paper, we present a two-dimensional （2D） fully analytical model with consideration of polarization effect for the channel potential and electric field distributions of the gate field-plated high electron mobility transistor （FP-HEMT） on the basis of 2D Poisson＇s solution. The dependences of the channel potential and electric field distributions on drain bias, polarization charge density, FP structure parameters, A1GaN/GaN material parameters, etc. are investigated. A simple and convenient approach to designing high breakdown voltage FP-HEMTs is also proposed. The validity of this model is demonstrated by comparison with the numerical simulations with Silvaco-Atlas. The method in this paper can be extended to the development of other analytical models for different device structures, such as MIS-HEMTs, multiple-FP HETMs, slant-FP HEMTs, etc.     

Relativistic treatment of the spin-zero particles subject to the second Poschl-Teller-like potential

The three-dimensional Klein-Gordon equation is solved for the case of equal vector and scalar second Poschl-Teller potential by proper approximation of the centrifugal term within the framework of the asymptotic iteration method. Energy eigenvalues and the corresponding wave function are obtained analytically. Eigenvalues are computed numerically for some values of n and It is found that the results are in good agreement with the findings of other methods for short-range potential.     

Global dynamical analysis of vibrational manifolds of HOCl and HOBr under anharmonicity and Fermi resonance:the dynamical potential approach

The vibrational dynamics of HOCl and HOBr between bending and OCl/OBr stretching coordinates with anharmonicity and Fermi coupling is studied with the classical dynamical potential approach. The quantal vibrational dynamics is mostly mapped out by the classical nonlinear variables such as fixed points, except for the state energies, which are quantized. This approach is global in the sense that the focus is on a set of levels instead of individual ones. The dynamics of HOBr is demonstrated to be less complicated. The localized modes along the OCl/OBr stretching coordinates are also shown to have O-Br bonds more prone to dissociation.     

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.