A two-page note on transition amplitudes. Obviously, a premature and incomplete pilot of a planned series, with two further sins committed. First, the idea itself has already been presented and illustrated earlier, via $V = x^2$. This observation is now extended, on the level of an easy student's exercise, to $V = x^2 +l(l+1)/x^2$. Second, the bulk of the text basically comprises just a summary of formulae while their derivation and all the innovative technical details which could, hopefully, make this message worth reading are just announced as to be described in an unspecified future publication [6]. MR2436429 Popov, V. S.; Trusov, M. A. Feynman operator calculus and singular quantum oscillator. Phys. Lett. A 372 (2008), no. 32, 5274--5275. 81R05 (81S99)