Strongly convergent method to solve one-dimensional quantum problems

Vargas et al. [Phys. Rev. E 53, 1954 (1996)] presented a numerical matrix method to solve the one-dimensional Schrodinger equation subject to Dirichlet boundary conditions. It is a well-known fact that the eigensolutions of such a confined system converge asymptotically to those of the corresponding unbounded problem as the boundary value increases. However, it is verified computationally that the results given by Vargas et al. are inaccurate, especially for the excited states of the perturbed oscillator Hamiltonian