content_image/319443.jpg content_image/319444.jpg content_image/319445.jpg
with 

<img src='content_image/319443.jpg'>

Where primes denote derivatives with respect to x and the PDM-Schr¨ odinger equation in (5) is known as the target equation. Obviously, as α, β, and γ change within constraint (2), a profile change of ˜ V ( x ) in (6) is unavoidable (hence, an ordering ambiguity conflict erupts in the process). Consequences of a point- canonical-transformation (PCT) mapping (often mediates a transition between two different effective potentials) on such a PDM particle are also discussed in section 2. Therein, we shall witness that such a mass setting results in an effective reflectionless modified P¨ oschl-Teller type potential well (cf. e.g., [20, 37]). We conclude in section 3. 

## 2 Consequences of PCT-mapping 

Following the well known PCT recipe (cf., e.g., [19,24;27]) would, with a sub- stitution of the form ψ ( x ) = m ( x ) 1 / 4 φ ( q ( x )) in (5), result in q ′ ( x ) = √ m ( x ) and suggests the following point canonical transformation 

with m ( x ) given in (4). Consequently, the PDM-Schr¨ odinger equation (5) is mapped into 

<img src='content_image/319444.jpg'>

<img src='content_image/319445.jpg'>

