Numerical regularization of Klauder effect in QLM

The numerical solution of the spiked harmonic oscillator in quantum mechanics within the framework of the Quasilinearization Method (QLM) is investigated systematically for different degrees of singularity αα and different coupling constants λλ. Several numerical algorithms consisting of different regularizations of the QLM differential equation and different nonlinear integration point distributions are studied. A simple algorithm that works uniformly across a large αα, λλ parameter space limited only by machine precision is proposed. The algorithm uses a single weak parameter which results are almost independent upon, accelerates the integration of the differential equations, and provides an automatic prescription for treating singular and regular potentials using the same methods.