  We study the recently proposed Lorentz-violating dispersion relation for
fermions and show that it leads to two distinct cubic operators in the
momentum. We compute the leading order terms that modify the non-relativistic
equations of motion and use experimental results for the hyperfine transition
in the ground state of the ${}^9\textrm Be^+$ ion to bound the values of the
Lorentz-violating parameters $\eta_1$ and $\eta_2$ for neutrons. The resulting
bounds depend on the value of the Lorenz-violating background four-vector in
the laboratory frame.
