Abstract: Starting from Voe Neumann's axiomatic system of quantum mechanics, this paper calculates the probability distributions of the kinetic and potential energy of the one-dimensional harmonic oscillator and the particle in one-dimensional infinitely deep square potential well. The results are compared with the classical cases, and it is shown that their relation conforms to Bohr's correspondence principle.
Then we put forward a new viewpoint:it seems that the concept of the total energy of the particle in quantum mechanics should be deliberated again; the two basic hypotheses in quantum mechanics-"Bohr's probabilistic interpretation" and "the postulate that the particle's energy eguals the eigenvalue in the energy eigenstate" ars not logically harmonious. At the same time, the limitation of von Neumann's axiomatic system is pointed out.