A new approach to the quantum KdV

We present a new formulation for the quantum evolution equation of KdV type. It is shown explicitly that a generalization of the usual recursion operator is possible, even when we follow the rules of quantization and assume that the nonlinear field variables do not commute. We also demonstrate that this recursion operator generates in a recursive way an infinite number of Hamiltonians commuting with each other, thus giving a basis for the complete integrability of the quantum mechanical evolution of the field. It is discovered that the reason why the recursion operator for the quantum KdV was not discovered earlier lies in the fact that this recursion operator is more closely connected to the general theory of the KP than to that of the KdV.