Effective Mass Dirac Equation Research Articles

Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential

We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass functionm(x). We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.

Approximate solutions to a spatially-dependent mass Dirac equation for modified Hylleraas plus Eckart potential with Yukawa potential as a tensor

In presence of spin (pseudo-spin) symmetry, approximate bounded fermionic (anti-fermionic) states of the effective mass Dirac equation for modified Hylleraas plus Eckart potential within Yukawa tensor interaction have been studied by means of the parametric Nikiforov–Uvarov method. We have obtained the analytical relativistic energy eigenvalues and their corresponding normalized two-spinor components of the wave functions in closed form by making an appropriate approximation to centrifugal (pseudo-centrifugal) term for any spin–orbit quantum number κ. Some special cases for various potential models have been investigated in relativistic and nonrelativistic limit. Further, numerical results for energy eigenvalues have been obtained within the exact spin and pseudo-spin symmetries.

Massive Dirac equation in asymmetric Hulthén potential

One-dimensional effective mass Dirac equation is solved in asymmetric Hulthén potential. Scattering and bound state solutions are obtained in terms of hypergeometric functions. Transmission and reflection coefficients are calculated by matching conditions on the wave function. The necessary conditions for the existence of transmission resonances and supercriticality are derived.

Approximate Solutions to the Dirac Equation with Effective Mass for the Manning–Rosen Potential in N Dimensions

The solutions of the effective mass Dirac equation for the Manning–Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac–Manning–Rosen problem for α = 0 or α = 1. In this case, the Manning–Rosen potential reduces to the Hulthen potential.

Effective-mass Dirac equation for Woods-Saxon potential: Scattering, bound states, and resonances

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and it is observed that the expressions for bound states and resonances are equal for the energy values E = ±m.

Dirac equation with position-dependent effective mass and solvable potentials in the Schrödinger equation

We study the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the framework of the position-dependent effective mass Dirac equation. The Dirac equation is mapped into the exactly solvable Schrödinger-like equation endowed with position-dependent effective mass that we present a new procedure to solve it. The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the mass function and then by using the obtained mass function, the imaginary potential can be obtained. The spinor wavefunctions for some of the obtained electrostatic potentials are given in terms of orthogonal polynomials. We also obtain the relativistic bound state spectrum for each case in terms of the bound state spectrum of the solvable potentials.

Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any κ-value

Abstract The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.

Exact Solutions of Effective Mass Dirac Equation with Non-PT-Symmetric and Non-Hermitian Exponential-type Potentials

By using a two-component approach to the one-dimensional effective mass Dirac equation, bound states are investigated under the effect of two new non-PT-symmetric and non-Hermitian exponential type potentials. It is observed that the Dirac equation can be mapped into a Schrödinger-like equation by rescaling one of the two Dirac wave functions in the case of the position-dependent mass. The energy levels and the corresponding Dirac eigenfunctions are found analytically.

Relativistic Confinement of Neutral Fermions with Partially Exactly Solvable and Exactly Solvable PT-Symmetric Potentials in the Presence of Position-Dependent Mass

The relativistic problems of neutral fermions subject to a new partially exactly solvable PT-symmetric potential and an exactly solvable PT-symmetric hyperbolic cosecant potential in 1+1 dimensions are investigated. The Dirac equation with the double-well-like mass distribution in the background of the PT-symmetric vector potential coupling can be mapped into the Schrodinger-like equation with the partially exactly solvable double-well potential. The position-dependent effective mass Dirac equation with the PT-symmetric hyperbolic cosecant potential can be mapped into the Schrodinger-like equation with the exactly solvable modified Poschl-Teller potential. The real relativistic energy levels and corresponding spinor wavefunctions for the bound states have been given in a closed form.

Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass

Abstract We present a new method to construct the exactly solvable PT-symmetric potentials within the framework of the position-dependent effective mass Dirac equation with the vector potential coupling scheme in 1 + 1 dimensions. In order to illustrate the procedure, we produce three PT-symmetric potentials as examples, which are PT-symmetric harmonic oscillator-like potential, PT-symmetric potential with the form of a linear potential plus an inversely linear potential, and PT-symmetric kink-like potential, respectively. The real relativistic energy levels and corresponding spinor components for the bound states are obtained by using the basic concepts of the supersymmetric quantum mechanics formalism and function analysis method.

Trapping neutral fermions with a PT-symmetric trigonometric potential in the presence of position-dependent mass

Abstract The relativistic problem of neutral fermions subject to PT-symmetric trigonometric potential ( ∼ i α tan α x ) in 1 + 1 dimensions is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Dirac equation with the vector coupling scheme and obtain the bound state solutions in closed form. The behavior of the energy spectra is discussed in detail.

Position-dependent effective mass Dirac equations withPT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1+1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen–Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.