  We attempt to shed light on the following question: What happens to the
negative energy states when we take the non-relativistic limit of the Dirac
equation? The Levy-Leblond equation is the non-relativistic limit of the Dirac
equation and describes fermions in the non-relativistic limit. The Levy-Leblond
equation includes singular matrices and an attempt to write the Hamiltonian
appears to show that the negative energy states are "buried" under an infinity.
We attempt to isolate the infinite energy states and also present an equivalent
way of viewing the Schrodinger dispersion relation. We propose that the
Levy-Leblond equation can also be seen as resulting from the contribution of
enhanced Lorentz violating terms to the Dirac equation.
