We calculate the polarization of the quantum and classical electrons confined in a one‐dimensional infinite potential well in the presence of a static electric field. As the external field is increased, the polarization always increases for a quantum electron in the ground state, but the polarization of an electron in any excited state decreases for a weak field and increases after passing a minimum. The polarization of a classical electron with nonzero initial kinetic energy is similar to the response of a quantum electron in excited states. The polarization determined by the diffusion equation is similar to the polarization of a quantum electron in the ground state.