The harmonic-potential theorem (HPT)[1] plays a significant role in the time-dependent phenomenon of quantum many-body systems due to its exact and analytical description of the change of the wave function under the influence of an arbitrary exteal electrical field.Furthermore,it is universal in the sense that it is applicable for any kind of form of interaction between the particles.The HPT has been widely employed in time-dependent theories such as the time dependent density functional theory (TDDFT),[2] time dependent quantal density functional theory (TD Q-DFT)[3,4] and also in Bose-Einstein condensation.[5]In the past decades,along with the fast development of research topics such as quantum computations and quantum information,[6] where using exteal fields to control the states of the quantum systems becomes more and more important,the HPT is expected to become a more fundamental theorem and has wider applications in those areas as well.Hence,the study of the theorem itself is also significant in its own right.In this Letter,we develop a new proof which is different from the operator method in Ref.[3].This opens a new venue to investigate the HPT in the presence of a static magnetic field.