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arXiv · 0905.0842

On the phase-integral method for the radial Dirac equation

Giampiero Esposito·Pietro Santorelli
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Abstract

In the application of potential models, the use of the Dirac equation in central potentials remains of phenomenological interest. The associated set of decoupled second-order ordinary differential equations is here studied by exploiting the phase-integral technique, following the work of Froman and Froman that provides a powerful tool in ordinary quantum mechanics. For various choices of the scalar and vector parts of the potential, the phase-integral formulae are derived and discussed, jointly with formulae for the evaluation of Stokes and anti-Stokes lines. A criterion for choosing the base function in the phase-integral method is also obtained, and tested numerically. The case of scalar confinement is then found to be more tractable.

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Giampiero Esposito, Pietro Santorelli. 2009-07-30. On the phase-integral method for the radial Dirac equation. https://doi.org/10.1088/1751-8113%2F42%2F39%2F395203

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