It is shown that von Neumann-Landau equation for wave functions can present amathematical formalism of motion of quantum mechanics. The wave functions ofvon Neumann-Landau equation for a single particle are `bipartite', in which theassociated Schr\"{o}dinger's wave functions correspond to those `bipartite'wave functions of product forms. This formalism establishes a mathematicalexpression of wave-particle duality and that von Neumann's entropy is aquantitative measure of complementarity between wave-like and particle-likebehaviors. Furthermore, this extension of Schr\"{o}dinger's form suggests thatcollapses of Schr\"{o}dinger's wave functions can be regarded as thesimultaneous transition of the particle from many levels to one.
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