On the transition probability for a quantum dot in a time dependent magnetic field

In this work we analyze in detail the dynamical behavior of a quantum dot in presence of a uniform time-dependent magnetic field, in the effective mass approximation. An exact solution for the time-evolved wave function is obtained when the initial state is a particular Fock-Darwin state. Moreover, we calculate the transition probability from an initial Fock-Darwin state to a given final Fock-Darwin state for the case of a magnetic field that changes linearly in time, flipping its direction.