  In this work, we study the modified Dirac equation in the framework of very
special relativity (VSR). The low-energy regime is accessed and the
nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is
similar to that achieved from the Standard Model Extension (SME) via coupling
of the spinor field to a Lorentz-violating term, but new features arise
inherited from the non-local character of the VSR. In addition, the
implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen
atom are determined by calculating the first-order energy corrections in the
context of standard quantum mechanics. Among the results, we highlight that the
modified Hamiltonian provides non-vanishing corrections which lift the
degeneracy of the energy levels and allow us to find an upper bound upon the
VSR-parameter.
