  An differential equation for wave functions is proposed, which is equivalent
to Schr\"{o}dinger's wave equation and can be used to determine energy-level
gaps of quantum systems. Contrary to Schr\"{o}dinger's wave equation, this
equation is on `bipartite' wave functions. It is shown that those `bipartite'
wave functions satisfy all the basic properties of Schr\"{o}dinger's wave
functions. Further, it is argued that `bipartite' wave functions can present a
mathematical expression of wave-particle duality. This provides an alternative
approach to the mathematical formalism of quantum mechanics.
