Solution of the Dirac Equation for Potential Interaction

Details Solution of the Dirac Equation for Potential Interaction Solution of the Dirac Equation for Potential Interaction

2002-11-20

arxiv.org/abs/math-ph/0211049v2

Int. J. Mod. Phys. A 18, 4955 (2003)

Physics

Mathematical Physics

19 pages, 4 tables; corrections in v2 mainly in parameters ("alpha" to "lambda-bar", the Compton wavelength)

Scientific paper

10.1142/S0217751X03015751

An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like equation for the spinor components that could simply be solved by correspondence with well-known exactly solvable non-relativistic problems. Taking the nonrelativistic limit will reproduce the nonrelativistic problem. The approach has been used successfully in establishing the relativistic extension of all classes of shape invariant potentials as well as other exactly solvable nonrelativistic problems. These include the Coulomb, Oscillator, Scarf, Poschl-Teller, Woods-Saxon, etc.

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