content_image/317177.jpg content_image/317175.jpg content_image/317174.jpg content_image/317176.jpg content_image/317178.jpg content_image/317179.jpg
where 

with 

One may then use (7) and substitute 

in (9) to imply 

<img src='content_image/317177.jpg'>

Which, in turn, would lead to an over simplified reference Schr¨ odinger equation of the form 

where 

Remarkably, the ”shifted-by-a-constant” potential well in (12) is known to be reflectionless/transparent (at any energy) with a reflection coefficient equals zero if λ > 1 is a positive integer (cf., e.g., Lekner [21] and/or Diaz et al. [25] for a comprehensive and detailed study on this potential). Therefore, a quick recollection to the essentials of the Modified P¨ oschl-Teller potential by Diaz et al. [25] would (with a bound state solution when E < 0 ) provide a clear 

<img src='content_image/317175.jpg'>

<img src='content_image/317174.jpg'>

<img src='content_image/317176.jpg'>

<img src='content_image/317178.jpg'>

<img src='content_image/317179.jpg'>

