The collocation method based on a generalized inverse multiquadric basis for bound-state problems

The generalized inverse multiquadric basis function (1 + c²∥x∥²)-^β/2, where c > 0, β > d, and x ∈ ℝ^d, is introduced for numerically solving the bound-state Schrödinger equation. Combined with the collocation method, this basis function can yield accurate eigenvalues of highly excited vibrations, as demonstrated by using one-and two-dimensional potentials. In addition, the generalized inverse multiquadric basis function is as flexible and simple as the Gaussian basis. The multiquadric form does not call for semiclassically distributed grid points and specially scaled exponential parameters as required in the latter case to achieve high accuracy.