Integration of operator differential equations

In a previous paper we introduced a method for obtaining exact solutions to the operator differential equations of quantum mechanics. In that paper we showed how to solve some simple quantum-mechanical models and we suggested that the method could be used to obtain exact solutions to the operator differential equations of more complicated models, such as the anharmonic oscillator whose Hamiltonian is H=1/2p²+1/4q⁴. In this paper we further sharpen the formalism and introduce the concept of a minimal solution. We then obtain the exact minimal solution to the operator differential equations arising from two different anharmonic-oscillator models whose Hamiltonians are H=1/2p²+1/4q⁴ and H=1/4p⁴+1/4q⁴.