Abstract
In (2+1)-dimensional space the exact solutions of the Dirac equation with cutoff Coulomb potential that takes into account the nucleus size is obtained in the under critical region of the discrete spectrum. Solutions of the Dirac equation in a strong external field arc obtained in the WKB approximation. A field is considered strong if the electron binding energy exceeds 2mc 2 and the descrete spectrum levels may be lowered into the lower continuum. The wave functions in the classically allowed and forbidden regions are found and the conditions for matching them on transition through the turning point are obtained. The WKB method is applied to the following problems: 1) generalization of the Bohr-Sommerfeld quantization conditions with allowance for relativistic effects and the spin in 2+1 dimensions: 2) finding energy and width of the quasistationary level in the lower continuum.
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