content_image/313835.jpg content_image/313833.jpg content_image/313836.jpg content_image/313834.jpg content_image/313832.jpg
with M ( ρ, ϕ, z ) = M ( ρ ) = ρ − 2 and subjected to an interaction potential of the form 

would admit exact energy eigenvalues given by 

<img src='content_image/313835.jpg'>

Obviously, the condition ( √$_{D/ϵ}$ − ˜ n$_{z}$ − 1 2 ) > 0 is manifested here and ought to be enforced, otherwise complex pairs of energy eigenvalues are obtained in the process. 

Moreover, a quantum particle with M ( ρ, ϕ, z ) = M ( ρ ) = ρ − 2 subjected to an interaction potential 

would indulge the exact energy eigenvalues 

<img src='content_image/313833.jpg'>

## 3.3 P T -symmetrized ˜ V ( z ) spectral signatures 

We may now consider a PT -symmetrized ˜ V ( z ) Scarf II in (18) so that 

where the corresponding Hamiltonian is known to be a non-Hermitian PT - symmetric Hamiltonian that admits exact eigenvalues (cf., e.g., Mustafa and 

<img src='content_image/313836.jpg'>

<img src='content_image/313834.jpg'>

<img src='content_image/313832.jpg'>

