Exact solutions of the Kemmer equation for a Dirac oscillator

Exact solutions of Kemmer equation for charged, massive, spin-1 particles in the Dirac oscillator potential have been found. The eigensolutions of this potential have been calculated and discussed in both natural and unnatural parities.     

On the Dirac oscillator

In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra C?₇. The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit.     

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.     

Path integral for one-dimensional Dirac oscillator

In this paper we derive the propagator for the one-dimensional Dirac oscillator using the supersymmetric path integral formalism. The spin calculations are carried out with the help of the technique of Grassmann functional integration. The Green function is exactly evaluated. The Polyakov spin factor is explicitly derived and the energy spectrum and the corresponding wave functions are deduced. PACS 03.65.Ca; 03.65.Db; 03.65.Ge; 03.65.Pm     

Integration method for the Dirac equation

An integration method for the Dirac equation is proposed. The method, based on diagonalization, reduces the problem to one of integration of independent second-order differential equations.     

Dirac equation with cylinder-symmetrical potential

For a potential V(?), $\text{?=(x}{}^2\text{+y}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, the Dirac equation is reduced to a pair of first-order differential equations in ?. The fine structure of relativistic “channeling” electrons bound to a crystal axis is calculated.     

On the Dirac equation

A connection is established between solutions of the Dirac equation (for an electron in a constant magnetic field) and those of the wave equation for a particle with zero mass.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 96–100, December, 1973.     

Pseudospin symmetry of the Dirac equation for a Mobius 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.     

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.     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Solution of the Dirac equation in the tridiagonal representation with pseudospin symmetry for an anharmonic oscillator and electric dipole ring-shaped potential

An anharmonic oscillatory potential is proposed in which a noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by the diagonalization of the radial recursion relation. The algebraic properties of the energy equation are also discussed, showing the exact pseudospin symmetry.     

Exact solution of the Dirac equation with a central potential

The exact solution of the Dirac equation with a central potential, in the semi-relativistic approximation, is derived and formulae for phase shifts and eigenvalue equations are given.     

Meson spectra with a power-law potential in the Dirac equation

A power law potential which is an equal admixture of scalar and vector parts with effective powerv ∞ 1/m _q , is proposed as a quark confining potential in the Dirac equation. The model is capable of predicting the meson spectroscopy encompassing both light and heavy quark-antiquark systems in a unified way.     

Quantum-classical correspondence of the Dirac equation with a scalar-like potential

Quantum matrix elements of the coordinate, momentum and the velocity operator for a spin-1/2 particle moving in a scalar-like potential are calculated. In the large quantum number limit, these matrix elements give classical quantities for a relativistic system with a position-dependent mass. Meanwhile, the Klein-Gordon equation for the spin-0 particle is discussed too. Though the Heisenberg equations for both the spin-0 and spin-1/2 particles are unlike the classical equations of motion, they go to the classical equations in the classical limit.      

A diffusion model for the Dirac equation

In previous work the author was able to derive the Schrödinger equation by an analytical approach built around a physical model that featured a special diffusion process in an ensemble of particles. In the present work, this approach is extended to include the derivation of the Dirac equation. To do this, the physical model has to be modified to make provision for intrinsic electric and magnetic dipoles to be associated with each ensemble particle.     

Strong Levinson theorem for the Dirac equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E= +m and E= -m to the number of states that have left the positive energy continuum or joined the negative energy continuum, respectively, as the potential is turned on from zero.