Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-02
J.Phys.A32:5643-5655,1999
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, plain Tex. In the final version, a section has been added, and the presentation has been improved
Scientific paper
10.1088/0305-4470/32/30/310
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown to involve a squared Dirac operator for the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle criterion, and a `perturbation' resulting from the potential. One then finds that a potential of Coulomb type in the Dirac equation leads to a potential term in the above second-order equations which is not even infinitesimally form-bounded with respect to the free operator. Moreover, the conditions ensuring essential self-adjointness of the second-order operators in the interacting case are changed with respect to the free case, i.e. they are expressed by a majorization involving the parameter in the Coulomb potential and the angular momentum quantum number. The same methods are applied to the analysis of coupled eigenvalue equations when the anomalous magnetic moment of the electron is not neglected.
Esposito Giampiero
Santorelli Pietro
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