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Keywords: Power-law, Position-dependent-mass, cylindrical coordi- nates, separability, exact solvability, spectral signatures 

## 1 Introduction 

The von Roos Hamiltonian [1] is known to describe quantum particles with position-dependent-mass (PDM), M ( ⃗ r ) = m$_{◦}$m ( ⃗ r ). Over the last few decades, the position-dependent-mass Hamiltonians have inspired research attention [2- 32] because of their applicability in the study of many-body problem, semicon- ductors, quantum dots, quantum liquids, etc. The kinetic energy operator in the von Roos Hamiltonian (with m$_{◦}$ = ℏ = 1 units) 

<img src='content_image/306232.jpg'>

admits an ordering ambiguity manifested by the non-uniqueness representation of the kinetic energy operator. Which would, in effect, introduce a profile change in the effective potential as the values of the parameters α , β , and γ change [cf., e.g., 25-29]. Here, α , β , and γ are called the von Roos ordering ambiguity parameters satisfying the von Roos constraint α + β + γ = − 1 . Nevertheless, an interesting and comprehensive background on the issue of consistency and usefulness of the position-dependent mass Schr¨ odinger equation was given by L˙evy-Leblond [32]. Therein, his work is devoted to sustaining and strengthening the conclusions that not only the use of position-dependent mass gives correct approximation, but its also a conceptually consistent approach. 

It is however constructive to mention that the continuity conditions at the abrupt heterojunction between two crystals implied that α = γ , otherwise for α ̸ = γ the wavefunctions vanish at the boundaries and the heterojunction plays the role of impenetrable barrier (cf., e.g., Mustafa and Mazharimousavi [10] 

