In this paper, we show that in two dimensions quantum mechanics can be mapped onto classical mechanics, by transforming the Schr\odinger equation into system of
n linear equations known as Kirchhoff equations. These Kirchhoff equations equations satisfy the a poison bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that quantum mechanics is consistent with classical mechanics atleast in two dimensions. This allows us to address the wave particle duality in terms of relative phase. As an illustration we show that the equation for optical vortices can be derived as Kirchhoff equation admit a paraxial wave equation in presence of real constant background.