Physics – Mathematical Physics
Scientific paper
2010-02-19
J. Phys. A: Math. Theor.43:325302, 2010; J.Phys.A43:325302,2010
Physics
Mathematical Physics
Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comment
Scientific paper
10.1088/1751-8113/43/32/325302
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.
Arda Altug
Biondini S.
Panella Orlando
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