The effective mass approximation (EMA), when applied to graded crystals, needs a modified from [GRAHICS] for the kinetic energy operator, where 2-alpha + beta = -1 and m(z) is the position-dependent effective mass. We have analyzed the energy dispersion of the EMA Hamiltonian, and performed a one-dimensional and a three-dimensional exact calculation to determine the proper value of beta. Our conclusion is that when beta = -1 the EMA provides better agreement with the exact solutions.