-$_{5}$ 5 x -$_{0.15}$ -$_{0.10}$ -$_{0.05}$ 0.05 0.10 0.15 $_{Re}$@$_{u}$$_{2}$ H$_{x}$LD -$_{5}$ 0 5 x 0.05 0.10 0.15 0.20 r H$_{x}$L -$_{5}$ 5 x -$_{0.4}$ -$_{0.2}$ 0.2 0.4 $_{Re}$@$_{u}$$_{1}$ H$_{x}$LD -$_{5}$ 0 5 x 0.05 0.10 0.15 0.20 r H$_{x}$L FIG. 5: The case of position dependent mass. Upper panel: plot of the normalized wave function Re [ u$_{1}$ ] and of the probability density for E = − 0 . 633251 (ground state); Lower panel: the same, but for E = +0 . 605869 (highest excited state). The model parameters are: m$_{0}$ = 1, W = 2, a = 10 and L = 2. We do not address further the issue of super-criticality within the position dependent mass case as it goes beyond the scope of the present work. Finally in Fig 7 we give a further example in the case of the position dependent mass when the potential well is deeper, W = 3, with the other parameters as in Figure 5. We note that in this case the highest level is close to the continuum ( E = m$_{0}$ = 1) and indeed the wave function converges less rapidly and the probability density as well. We have computed for example that in this case the probability of the particle to be outside the potential well ( | x | > 2) is: P$_{outside}$ ≈ 0 . 57 which is even greater of the probability to be inside ( − L ≤ x ≤ L ) is: P$_{inside}$ ≈ 0 . 43. The less rapid convergence of the wave function is due to the fact that the coefficient that controls such behavior (in this case as x → ∞ ,φ$_{R}$ ( x ) ≈ e − $^{νax}$) is ν = $^{√}$E 2 − m 2 $_{0}$/a , and therefore very small giving a wave function that vanishes much slower than those corresponding to the lowest lying bound states. 20