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In a previous paper$^1$, submitted to Journal of Physics A -- we presented aninfinite class of potentials for which the radial Schr\"odinger equation atzero energy can be solved explicitely. For part of them, the angular momentummust be zero, but for the other part (also infinite), one can have any angularmomentum. In the present paper, we study a simple subclass (also infinite) ofthe whole class for which the solution of the Schr\"odinger equation is simplerthan in the general case. This subclass is obtained by combining anotherapproach together with the general approach of the previous paper. Once this isachieved, one can then see that one can in fact combine the two approaches infull generality, and obtain a much larger class of potentials than the classfound in ref. $^1$ We mention here that our results are explicit, and whenexhibited, one can check in a straightforward manner their validity

New classes of potentials for which the radial Schrödinger equation can be solved at zero energy: II