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We formulated the oscillators with position-dependent finite symmetric decreasing and increasing mass. The classical phase portraits of the systems were studied by analytical approach (He’s frequency formalism). We also study the quantum mechanical behaviour of the system and plot the quantum mechanical phase space for necessary comparison with the same obtained classically. The phase portrait in all the cases exhibited closed loop reflecting the stable system but the quantum phase portrait exhibited the inherent signature (cusp or kink) near origin associated with the mass. Although the systems possess periodic motion, the discrete eigenvalues do not possess any similarity with that of the simple harmonic oscillator having m = 1.

New technique suggested by Almeida and Martin, can be only used to calculate eigenvalues of single well oscillators. As such the method will fail drastically even to compute eigenvalues of single properly non-linear oscillator of the type H = p 2 + x 2 + x 2 > x 4 . Further new technique can hardly ever be used to calculate eigenvalues of any double-well oscillator. Without the calculation of wave characteristics mod square | Ψ | 2 or oblique way by way of expectation value A > the stated paper loses its intention as widely usual method in eigenvalue relation.

We study spectral behaviour of linear operator using matrix diagonalisation method and notice that spectral breaking is an inherent behaviour in PT -symmetry .