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We analyze the Majorana equation in the limit where the particle is at rest.We show that several counterintuitive features, absent in the rest limit of theDirac equation, do appear. Among them, Dirac-like positive energy solutionsthat turn into negative energy ones by free evolution, or nonstandardoscillations and interference between real and imaginary spinor components forcomplex solutions. We also study the ultrarelativistic limit, showing that theMajorana and Dirac equations mutually converge. Furthermore, we propose aphysical implementation in trapped ions.

The nonrelativistic limit of the Majorana equation and its simulation in trapped ions