One may then use (7) and substitute in (9) to imply 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 5 V$_{eff}$ ( q ) = g$_{1}$ m $^{′′}$( x ) m ( x ) 2 − g$_{2}$ m $^{′}$( x ) 2 m ( x ) 3 , (9) g$_{1}$ = 1 4 (1 + 2 β ) , g$_{2}$ = α ( α + β + 1) + β + 9 16 . (10) x a = tanh ( q a ) ; | x | < a, (11) V$_{eff}$ ( q ) = − λ ( λ − 1) a $^{2}$cosh$^{2}$( q/a ) + 8 a 2 (3 g$_{1}$ − 2 g$_{2}$ ) ; λ ( λ − 1) = 4 (5 g$_{1}$ − 4 g$_{2}$ ) . (12) d $^{2}$φ ( q ) dq 2 + ( k 2 + µ 2 λ ( λ − 1) cosh $^{2}$( µq ) ) φ ( q ) = 0, (13) k 2 = E − 8 µ $^{2}$(3 g$_{1}$ − 2 g$_{2}$ ) = E ; µ = 1 /a . (14) where with