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tures of different ˜ V ( z ) potentials on the overall spectrum. 

## 3.1 The radial harmonic oscillator g ( ρ ) = bρ $^{2}$/ 2 

The choice of υ = 1 / 2 along with ˜ V ( ρ ) = a $^{2}$ρ$^{2}$/ 4 would imply that equation (14) reads 

and (15), in turn, yields 

Obviously, Eq.(17) has exact eigenvalues in the form 

and implies that 

We observe that an auxiliary constraint 

on the ambiguity parameters is manifested here by the requirement that E ∈ R . 

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