form continuous functions except at the origin x = 0 and are of a finite discon- tinuity, therefore. Under these settings, we may benefit from the well-known definitions associated with the Dirac delta distributions (cf., e.g., equations (4) and (5) of [36]). That is, if U ( x ) is a discontinuous function of x then the distributions U ( x ) δ ( x ) and U ( x ) δ $^{′}$( x ) can be rewritten as Which would imply (with U ( x ) = f $^{′}$( h ( x )) / f ( h ( x )) $^{2}$) that the effective po- tential in (9) can be recast as To avoid the physical and/or mathematical meaninglessness of δ ( x ) $^{2}$, two feasible solutions for (13) obtain. The simplest of which is achieved by taking G$_{1}$ = 0 and G$_{2}$ = 0 (i.e., Mustafa and Mazharimousavi’s [10], MM-, ordering ambiguity parameters α = γ = − 1 / 4 and β = − 1 / 2 here, where no other known-ordering in the literature may satisfy the G$_{1}$ = 0 = G$_{2}$ condition). In this case, the position-dependent-particle at hand (2) remains free and admits a free-particle solution, therefore. However, the triviality of such a choice (i.e., G$_{1}$ = 0 = G$_{2}$ ) inspires the search for yet another feasible solution for (13) where G$_{1}$ = 0 (i.e., β = − 1 / 2). If we just recollect that α + β + γ = − 1 (i.e., the von Ross constraint) and impose the continuity conditions at the abrupt heterojunction boundaries (i.e., simply the ordering ambiguity parameters α and γ are related through α = γ , a manifesto that ensures the continuity of m ( x ) $^{α}$ψ ( x ) and m ( x ) α + β [ ∂$_{x}$ψ ( x )] at the heterojunction boundary) along with the choice of (2 G$_{1}$ − G$_{2}$ ) = 0, we 6 U ( x ) δ ( x ) = U (0) δ ( x ) , (11) U ( x ) δ $^{′}$( x ) = U (0) δ $^{′}$( x ) − U $^{′}$(0) δ ( x ) . (12) V$_{eff}$ ( q ( x )) = G$_{1}$U (0) δ ′ ( x ) + (2 G$_{1}$ − G$_{2}$ ) f $^{′}$( h ( x )) 2 f ( h ( x )) 3 δ ( x ) $^{2}$. (13)