a Heaviside discontinuous functional nature have been discussed in the litera- ture (cf., e.g., [38-40]), but never within our forthcoming methodical proposal, at least. It would be interesting to subject such mass settings to the sequel theoretical experiment, therefore. We witness (in section 2) that a quasi-free quantum particle (i.e., subjected to V ( x ) = 0 whilst V$_{eff}$ ( q ( x )) = 0) endowed with the PDM-setting of (2) would experience scattering effects manifested by the particle’s by-product in- troduction of the derivative of the Dirac’s delta interaction δ $^{′}$( x ) as a result of a point canonical transformation (PCT) recipe (hence, the notion of self- scattering correspondence is unavoidable). The detailed solution of which can be inferred from the scattering potential V ( q ) = − aδ ( q ) + bδ $^{′}$( q ) of Gadella et al. [36] using proper parametric mappings into our model (see (14) below), of course. In this case, the reader may wish to refer to Gadella et al. [36] for the mathematical and/or physical details. Moreover, a new (the only feasibly ad- missible within the current methodical proposal) ordering ambiguity parameters set obtains in the process. We conclude in section 3. Under position-dependent-mass settings, the von Roos PDM Schr¨ odinger equa- tion [22-29] (in ℏ = m$_{◦}$ = 1 units) reads with 2 PCT recipe and self-scattering correspondence [ − 1 2 ∂$_{x}$ ( 1 m ( x ) ) ∂$_{x}$ + ˜ V ( x ) ] ψ ( x ) = Eψ ( x ) , (3) ˜ V ( x ) = g$_{1}$ m $^{′′}$( x ) m ( x ) 2 − g$_{2}$ m $^{′}$( x ) 2 m ( x ) 3 (4) 4