Use of operator wave functions to construct a refined correspondence principle via the quantum mechanics of Wigner and Moyal

We represent the momentum operator p by p+(h//2i)(∂/∂p) and the position operator q by q−(h//2i)(∂/∂p). We then apply each resulting operator that appears in the nonrelativistic quantum mechanics of Schrödinger and Heisenberg to the constant 1. What results is a Wigner–Moyal theory which is as complete as the usual Schrödinger–Heisenberg theory. Replacing Planck’s constant h/ by zero in the Wigner–Moyal theory results in the classical physics of Newton. We thereby obtain a refined correspondence principle.