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## 2 Cylindrical coordinates and separability 

Let us consider the kinetic energy operator of the PDM Hamiltonian in (1) and a PDM function of the form m ( ⃗ r ) = m ◦ M ( ρ, ϕ, z ) = M ( ρ, ϕ, z ) (where ℏ = m ◦ = 1 units are to be used hereinafter). Moreover, we consider the following substitutions 

to imply 

Using the above identities, one (with M ( ρ, ϕ, z ) ≡ M for simplicity of notations) may rewrite 

and 

<img src='content_image/307120.jpg'>

<img src='content_image/307118.jpg'>

<img src='content_image/307117.jpg'>

<img src='content_image/307119.jpg'>

