In this thesis We consider the effect of the Lorentz violation on an electron in a penning trap. For this purpose , free massive-fermion part of the Lorentz violation extension of the Lagrangian is considered. Consequently, the none relativistic Hamiltonian of the electron in the electromagnetic field is derived by using F.W. transformation. Finally we show that, there terms which can put better bound on the Lorentz violation parameters.
