On the quantization of yet another two nonlinear harmonic oscillators

In two previous papers the quantization was discussed of three one-degree-of-freedom Hamiltonians featuring a constant c, the value of which does not influence at all the corresponding classical dynamics (which is characterized by isochronous solutions, all of them periodic with period 2pi: "nonlinear harmonic oscillators"), but turned instead out to influence, possibly quite nontrivially, the results in the quantized case. The quantization of two analogous Hamiltonian systems is discussed in this paper. The outcome is analogous, if perhaps even more clear cut, than in the previous three cases; it also confirms that different quantized spectra may be obtained if quantization is performed before or after a (nonlinear) canonical transformation.