New exact solution of the one-dimensional Dirac equation for the Woods–Saxon potential within the effective mass case

Abstract

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.

Scattering and bound states for the Hulthén potential in a cosmic string background

“…Namely, we can add it directly to the mass term of the Dirac equation. The most common interpretation known in the literature for this coupling is that of a position-dependent effective mass [8].…”

Scattering State of Klein-Gordon Particles by q-Parameter Hyperbolic Poschl-Teller Potential

“…Equation (29) admits a solution if and only if its determinant is zero [30]. This thus provides a condition for getting the energy eigenvalues as …”

Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

“…The solution of the relativistic Dirac equation for quantum mechanical systems in cases of both spatially dependent mass and constant mass plays an important role in many branches of physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The Dirac equation with position dependent masshas attracted greater interest as its importance has been recognised [5][6][7][8][9][10][11][12][13][14][15].…”

“…The Dirac equation with position dependent masshas attracted greater interest as its importance has been recognised [5][6][7][8][9][10][11][12][13][14][15]. This equation has been addressed for solvable potentials by a number of different methods [19][20][21][22][23][24][25][26][27][28][29][30].…”