New exactly solvable periodic potentials for the Dirac equation
B. F. Samsonov, A. A. Pecheritsin, E. O. Pozdeeva, M. L. Glasser
Abstract
A new exactly solvable relativistic periodic potential is obtained by the periodic extension of a well-known transparent scalar potential. It is found that the energy band edges are determined by a transcendental equation which is very similar to the corresponding equation for the Dirac Kronig-Penney model. The solutions of the Dirac equation are expressed in terms of elementary functions.
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