while 1 − z ≈ e a ( x − L $^{)}$) : Upon defining as S, T, U, V respectively the various combinations of gamma functions appearing the above expressions the wave functions are written as: Now we have to match the two solutions in x = 0 requiring continuity of the wave-function φ$_{L}$ (0) = φ$_{R}$ (0) and of its first derivative φ ′ $_{L}$(0) = φ ′ $_{R}$(0). This gives the homogeneous system: which admits a solution only if its determinant is zero. This provides a condition for extracting the energy eigenvalue: When Eq. 52 is satisfied the relation between A ′ and D ′ is found to be: and A ′ is the usual normalization constant. The condition in Eq. (52) is a transcendental equation which can be solved numerically. We provide numerical examples of the bound states. As we are studying bound states we seek numerical solutions of Eq. (52) in the interval − W ≤ E ≤ m . Since F ( E ) = 0 is complex the energy eigenvalues E are found by solving numerically, for real solutions, the two (independent) equations Re[ F ( E )] = 0 and Im[ F ( E )] = 0. Fig. 4 shows graphically the details of the numerical computations both for the position dependent mass and the constant mass cases. In table I we give the numerical results for the spectra of the position dependent mass case and that of the constant mass case, with the same values of the parameters ( m$_{0}$ = 1; L = 2; a = 10; W = 2) in order to make a meaningful comparison between the two cases. For the case of the 18 D ′ = T V 2 ϵ − 1 2 ϵ + 1 e 2 $^{ϵaL}$A ′ = S U e − 2 ϵaL A ′ , F ( E ) = SV T U − e 4 ϵaL 2 ϵ − 1 2 ϵ + 1 = 0 . (52) A ′ $^{[}$S e − ϵaL + T e − (1 − ϵ ) aL $^{]}$− D ′ $^{[}$U e + ϵaL + V e − (1+ ϵ ) aL ] = 0 A ′ $^{[}$− ϵS e − ϵaL − (1 − ϵ ) T e − (1 − ϵ ) aL $^{]}$− D ′ $^{[}$− ϵU e + ϵaL + (1 + ϵ ) V e − (1+ ϵ ) aL ] = 0 φ$_{L}$ ( x ) ≈ A ′ $^{[}$S e − ϵa ( x + L ) + T e − (1 − ϵ ) a ( x + L ) ] (51a) φ$_{R}$ ( x ) ≈ D ′ $^{[}$U e − ϵa ( x − L ) + V e (1+ ϵ ) a ( x − L ) ] (51b) φ$_{L}$ ( x ) ≈ A ′ { Γ(1 + 2 ν )Γ(1 − 2 ϵ ) Γ(1 − ϵ + ν − λ )Γ(1 − ϵ + ν + λ ) e − ϵa ( x + L ) + Γ(1 + 2 ν )Γ( − 1 + 2 ϵ ) Γ( ϵ + ν + λ )Γ( ϵ + ν − λ ) e − (1 − ϵ ) a ( x + L ) } , φ$_{R}$ ( x ) ≈ D ′ [ Γ(1 + 2 ν )Γ(1 + 2 ϵ ) Γ(1 + ϵ + ν + λ )Γ(1 + ϵ + ν − λ ) e − ϵa ( x − L ) + Γ(1 + 2 ν )Γ( − 1 − 2 ϵ ) Γ( − ϵ + ν + λ )Γ( − ϵ + ν − λ ) e (1+ ϵ ) a ( x − L ) ] .