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2.2 ELECTRICAL, ELECTRONIC, INFORMATION ENGINEERING
We consider a method of solving the Dirac scattering problem based on an approach previously used by the authors to solve the Schrodinger scattering problem to develop a conditional exact scattering solution and an unconditional series solution. We transform the Dirac scattering problem into a form that facilitates a soltuion based on the relativistic Lippmann-Schwinger equation using the relativistic Green's function that is transcendental in terms of the scattered field. Using the Dirac operator, this solution is transformed further to yield a modified relativistic Lippman-Schwinger equation that is also transcendental in terms of the scattered field. This modified solution faclitates a condition under which the solution for the scattered field is exact. Further, by exploiting the simultaneity of the two solutions available , we show that it is possible to define an exact (non-conditional) series solution to the problem.
Blackledge, J., Babajanov, B. (2013) On the Dirac Scattering Problems. Mathematica Aeterna, vol: 3, ( 7), p. 535 - 544, 2013. doi:10.21427/D7JP6B