content_image/305020.jpg content_image/305026.jpg content_image/305024.jpg content_image/305022.jpg content_image/305021.jpg content_image/305023.jpg
where primes denote derivatives with respect to x and 

We now follow the well-known point-canonical-transformation (PCT) recipe (cf. e.g., [19]) through the substitution ψ ( x ) = m ( x ) 1 / $^{4}$φ ( q ( x )) in (3) to imply (with q $^{′}$( x ) = √ m ( x )) x x 

and obtain a Schr¨ odinger equation of the form 

where 

Which would in turn (with m $^{′}$( x ) = ∂$_{x}$m ( x ) , and f $^{′}$( h ( x )) = ∂ h ( x $_{)}$f ( h ( x )) ) yield 

<img src='content_image/305020.jpg'>

with 

Where δ ( x ) denotes Dirac delta function and δ $^{′}$( x ) = ∂$_{x}$δ ( x ) is the derivative of the Dirac delta function. Hereby, the terms associated with δ $^{′}$( x ) and δ ( x ) 2 

<img src='content_image/305026.jpg'>

<img src='content_image/305024.jpg'>

<img src='content_image/305022.jpg'>

<img src='content_image/305021.jpg'>

<img src='content_image/305023.jpg'>

