In this paper, we investigate the problem of fermion creation inside a three-dimensional cubic box. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider the box with oscillating walls and introduce the time evolution of the quantized field by expanding it over the instantaneous basis. We explain how we can obtain the average number of particles created. In this regard, we find the Bogoliubov coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity’s spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation and their dynamical Casimir energy.
