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Majorana equation and some of its solutions in 2 + 1 dimensions

A priori, spinning particles (let say of spin one-half) can be described both by the finite-component Dirac equation and the infinite-component Majorana equation. By considering these equations in the presence of an external electromagnetic field, one can discover differences in their solutions. In the present paper, whilst trying to answer the question of how important these differences are, we compare solutions of these equations for a charged particle moving in a constant uniform magnetic field, and compare power decomposition in 1/c and the nonrelativistic limit for both equations. We have found the Majorana energy spectrum of a charged particle in a constant uniform magnetic and how it differs from the corresponding Dirac spectrum. This difference can be, in principle, observed in adequate experimental conditions. We have demonstrated that within the nonrelativistic limit both equations are reduced to the Pauli equation. However, the difference between the Majorana and Dirac equations does exist and already starts to manifest itself in terms of the second order in 1/c.