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We have studied the intrinsic contribution to anomalous Hall conductivity in presence of the normal magnetic field. A semiclassical approach for calculating the Hall conductivity in presence of the nontrivial Berry phase is used. This method is based on the semiclassical equations of motion with anomalous velocity correction and the Boltzmann transport equation. We present the formulation of anomalous Hall conductivity in this approach. We perform explicit calculations for a two-dimensional system which is described by Dirac Hamiltonian. At zero magnetic field, our results coincide with previous results which are obtained both using the semiclassical method and Kubo formalism. For the strong magnetic field, Hall conductivity decreases as a power-law. The exponent of the power-law behavior for the infinite energy band is 1/3 and for the finite energy band, there is a crossover from 1/3 to1.

In this paper we calculate the Berry phase for a wave function of a particle in an infinite spherical potential well with adiabatically varying. In order to do this, we need the solutions of the corresponding Schrödinger equation with a time dependent Hamiltonian. Here, we obtain these solutions for the first time. In addition, we calculate the Berry phase in one dimensional case for an infinite potential well. We see that this phase is comparable with the usual dynamical phase but with different sign. Therefore, it is important to take it into account in the quantum mechanical calculations.