1 Introduction The von Roos Hamiltonian for position-dependent-mass (PDM) quantum par- ticles is known to be associated with an ordering ambiguity problem manifested by the non-unique representation of the kinetic energy operator [1]. In such Hamiltonian an obvious profile change in the effective potential is introduced when the para- metric values of the ambiguity parameters ( α, β, γ ) are changed (within the von Roos constraint α + β + γ = − 1). Nevertheless, it is known that the conti- nuity conditions at the heterojunction boundaries between two crystals imply α = γ (cf., e.g., ref.[2] and the related references cited therein) . This would effectively reduce the domain of the acceptable parametric values of the ambigu- ity parameters. In fact, the PDM Hamiltonian (1) is known to be a descriptive model for many physical problems (like but not limited to, many-body problem, electronic properties of semiconductors, etc.) [1-30]. It is, moreover, a math- ematically challenging and a useful model that enriches the class of exactly solvable quantum mechanical systems. In the literature, nevertheless, one may find many suggestion on the am- biguity parametric values. For example, Gora and William have suggested β = γ = 0 , α = − 1, Ben Daniel and Duke α = γ = 0 , β = − 1, Zhu and Kroemer α = γ = − 1 / 2 , β = 0, Li and Kuhn β = γ = − 1 / 2 , α = 0, and Mustafa and Mazharimousavi α = γ = − 1 / 4 , β = − 1 / 2 (cf., e.g., [2,3] and ref- erences therein). Very recently, we have studied the problem of a singular PDM particle in an infinite potential well and shown that none of the above known parametric ordering sets is admissible within the methodical proposal discussed 2 H = − ℏ 2 4 [ m ( ⃗ r ) γ ⃗ ∇ m ( ⃗ r ) β · ⃗ ∇ m ( ⃗ r ) α + m ( ⃗ r ) α ⃗ ∇ m ( ⃗ r ) β · ⃗ ∇ m ( ⃗ r ) γ ] + V ( ⃗ r ) , (1)