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

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 the Dirac equation, do appear, among which are Dirac-like positive energy solutions that turn into negative energy ones by free evolution, or nonstandard oscillations and interference between real and imaginary spinor components for complex solutions. We also study the ultrarelativistic limit, showing that the Majorana and Dirac equations mutually converge. Furthermore, we propose a physical implementation in trapped ions.