The collective excitations of a system, particularly at low temperatures, behave as quasi-particles with properties that may differ from their constituents.In particular, there are exotic excitations called Majorana fermions or zero-energy modes modes, which have the special characteristic of being their own antiparticle.In that sense, this work seeks tracing these excitations in an artificial arrangement of a nanowire simulated through a one-dimensional chain.In that direction, the Fourier transform is used with the purpose of bringing the Hamiltonian from position to momentum space.Subsequently, it is proposed to diagonalize the system using the Bogoliubov-de Gennes formalism.In this way, we obtain the phase diagram displaying the set of parameters for which zero energy modes are stabilized.