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constant mass we have used the results of [24]. We observe that the in the position dependent mass case the number of bound states decreases relative to the constant mass. In Figures 5 and 6 we provide some example of the (normalized) wave-functions and probability densities both for constant mass case and position dependent mass. Also, comparing Figure 5 with Figure 6 one can infer that in the position dependent mass case the probability density is almost flat in the region inside the potential well as opposed to the constant mass case where, for the highest excited states it oscillates strongly. We note, in the constant mass case (right panel of Fig.4), an eigenvalue corresponding to E = − m = − 1 which merges with the negative continuum. This situation has previously been considered in the literature [24, 29, 30] and has been referred to as super-criticality. Such super-critical states are also called half-bound states and are characterized by the fact that one of the spinor components (the upper, u$_{1}$ , or the lower, u$_{2}$ ) are not strictly normalizable. We show in table I the eigenvalue E = − 1 only because it is a solution of Eq. 52. 

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