The transformation characteristics of the probability amplitude corresponding to an arbitrary sublevel system of a nucleus is studied. The nucleus, with arbitrary spin, is placed in a magnetic and an electrostatic field and irradiated selectively. The possible physical implication of the above mentioned transformation characteristics is discussed. The differences between the two characteristics, i.e., the 2π or 4π symmetry of the wave functions under space rotation and the 2π or 4π periodicity of the probability amplitude corresponding to a sublevel system under selective irradiation are explained.