In due course, the position-dependent-mass jump of (1) implies It should be noted here that, in a straightforward manner, one may substitute U (0) in (18) to obtain the transmission and reflection coefficients (15) and (16), respectively, as and In this work, a quasi-free quantum particle (i.e., V ( x ) = 0 whereas V$_{eff}$ ( q ( x )) = 0) endowed with a position-dependent-mass jump (1) is considered. Whilst, un- der Mustafa’s and Mazharimousavi’s ordering ambiguity parametrization (i.e., α = γ = − 1 / 4 and β = − 1 / 2) the free PDM quantum particle remained free, we have witnessed (only under a specific though rather new set of ordering am- and 8 3 Concluding remarks q ( x ) = x √ f ( h ( x )) = x [1 + µ h ( x )] , (17) U ( x ) = µ 1 + µ h ( x ) = ⇒ U (0) = µ 1 + µ/ 2 . (18) R = − 4 µ (1 + µ/ 2) 2 4 (1 + µ/ 2) 4 + µ $_{2}$, (19) T = 4 (1 + µ/ 2) 4 − µ 2 4 (1 + µ/ 2) 4 + µ $_{2}$. (20) Consequently and asymptotically speaking, a Taylor series expansions about µ → 0 (i.e., 0 < µ << 1, also very likely experimentally feasibly applicable) would result in casting the reflection and transmission intensities, respectively, as | R | 2 ≈ µ 2 + O ( µ $^{3}$) and | T | 2 ≈ 1 − µ 2 + O ( µ $^{3}$) . Within such asymptotic tendencies, it is obvious that increasing the value of µ from just above 0 to 1 would make the derivative-of-the-Dirac’s delta scatterer less transparent until total reflection takes place when µ = 1.