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We focus on a recently developed generalized pseudospectral method foraccurate, efficient treatment of certain central potentials of interest invarious branches in quantum mechanics, usually having singularity. Essentiallythis allows optimal, nonuniform spatial discretization of the pertinentsingle-particle Schrodinger equation satisfying Dirichlet boundary conditionleading to standard diagonalization of symmetric matrices. Its validity andfeasibility have been demonstrated for a wide range of important potentialssuch as Hulth\'en, Yukawa, generalized spiked harmonic oscillators, Hellmann,Coulomb potentials without/with various perturbations (for instance, linear andquadratic) etc. Although initially designed for singular potentials, this hasalso been remarkably successful for various other cases such as power-law,logarithmic, harmonic potentials containing higher order perturbations, 3Drational potentials as well as confinement studies. Furthermore, a large numberof low-, moderately high-, high-lying multiply excited Rydberg states such assingly, doubly excited He as well as triply excited hollow $2l2l'2l'' (n \ge2)$ and $3l3l'3l''$ doubly-hollow resonances in many-electron atoms have beentreated by this approach within a KS DFT with great success. This offers veryhigh-quality results for both ground and higher lying states for arbitraryvalues of potential parameters (covering both weak and strong coupling) withequal ease and efficacy. In all cases, excellent agreement with literatureresults are observed; in many cases this surpasses the accuracy of all otherexisting results while in other occasions our results are comparable to thebest ones available in literature.

A general method for central potentials in quantum mechanics