In the past few years, the generalized pseudospectral (GPS) method, which is also known as the semispectral method or collocation method, has been successfully applied to investigate the structural properties of atomic and molecular systems,[1–5] the quantum scattering processes in nuclear and atomic physics,[6,7] and the laser-atom interactions.[8–10] Its usefulness has been continuously revealed in recent years in accurately and efficiently solving both the time-independent and time-dependent Schrödinger and Dirac equations. Being a type of discrete variable representation (DVR) method, the GPS method shows its special superiority over other generalizations of DVR, such as the finite difference and finite element methods. For example, the Numerov and Runge-Kutta methods, as in the latter case, are local approaches to the unknown function by a sequence of overlapping low-order polynomials in a small subset of user-defined grid points.[11,12] The GPS method and its variants in different forms are generally global approaches to the unknown function using global basis functions with a high degree, for example, the trigonometricfunctions or the orthogonal polynomials of a Sturm-Liouville problem.[6] It has also been shown that the GPS method can produce much smoother solutions with incredible exponential convergence, which is significantly accurate compared to other DVR methods.[13–15] The discretized character of the GPS method also lead to it being preferable in many aspects than the basis expansion method, which has been widely used in atomic and molecular physics. For instance, it does not require the computation of potential matrix elements, which sometimes is the most difficult and time-consuming part of the structural calculations.[3] The GPS method can also be easily implemented to solve the Schrödinger equation in the momentum space, keeping in mind that solving such a singular problem in the momentum space is sometimes a formidable task for the basis expansion method.[16]