would then dismiss the δ ( x ) 2 ambiguity. Under such conditions, a new set of ordering ambiguity parameters (the only feasibly admissible within the current methodical proposal, and the yet to be labeled as MM1-ordering, hereinafter) that casts α = γ = − 3 / 4 and β = 1 / 2 is obtained. As such and within this new set of ambiguity parameters, the effective potential (13) collapses into a simple form We clearly observe that a scattering problem of a quasi-free quantum particle (i.e., V ( x ) = 0 whereas V$_{eff}$ ( q ( x )) = 0) subjected to the derivative of the one- dimensional Dirac delta interaction (also called the point dipole interaction) is manifested by (14) of Hamiltonian (7) (hence, a self-scattering effect obtains in the process). The detailed solution of which can be inferred from the scattering coefficients of the V ( q ) = − aδ ( q ) + bδ $^{′}$( q ) potential of Gadella et al. [36] by taking m = 1, a = 0 and b = U (0) / 2 as proper parametric mappings into our model. Choosing to skip all the mathematical and/or physical details, the reflection and transmission coefficients (see Eq.(23) of [36]) would , respectively, read and In a straightforward manner it can be easily shown that the condition | R | 2 + | T | 2 = 1 is satisfied. Consequently, a free quantum particle endowed with the PDM-setting of (2) may very well experience scattering effects. Moreover, it is obvious that whilst a U (0) = 0 yields (although trivial) a totally transpar- ent/reflectionless derivative-of-the-Dirac’s delta scatterer, a U (0) = ± 2 yields a totally reflective derivative-of-the-Dirac’s delta scatterer. 7 R = − 4 U (0) 4 + U (0) 2 (15) T = 4 − U (0) 2 4 + U (0) 2 (16) V$_{eff}$ ( q ( x )) = U (0) 2 δ $^{′}$( x ) ; U ( x ) = f $^{′}$( h ( x )) f ( h ( x )) $_{2}$. (14)