3 Concluding Remarks parametric values associated with the available orderings in the literature, along with their classifications as to being admissible (i.e., λ > 2 ) or non-admissible (i.e., λ ≤ 2 ). In the same table, we list some new orderings that are feasibly admissible. Obviously, non of the orderings known in the literature can be labeled as admissible, i.e., λ > 2, (within our current methodical proposal, of course). We have considered the PDM-von Roos Hamiltonian for a quantum particle en- dowed with an unusual position-dependent mass function with two singularities in an infinite potential well. A point-canonical-transformation is used and an obvious correspondence between two effective (reference and target) Hamiltoni- ans is obtained. Apparently, the singular PDM settings led to (through a PCT) the reflectionless modified P¨ oschl-Teller potential well. The exact solution of which is known in different perspectives. We have followed Diaz et al. [25] to come out with the result that non of the available known orderings in the litera- ture is labeled admissible. Hereby, it should be noted that, our classifications on the ”admissibility” and ”non-admissibility” of the ordering ambiguity parame- ters (reported in table 1) are consequences of the boundary condition in (23). The validity of which resides only within the setting of the current methodical proposal associated with our model in (4). Nevertheless, one could re-scale k 2 of equation (2) of Lekner [21] for λ = ν +1, for example, and deduce all related reflectionless positive energy states, non- reflecting wave packets, etc. Yet, by re-scaling k 2 of equation (39.2) of Fl¨ ugge [37] for λ = ν +1, one would recycle Fl¨ ugge’s results. Consequently, we may con- clude that the ordering ambiguity conflict associated with the uniqueness of the kinetic energy operator does not only depend on the heterojunction boundaries 8