Quasilinearization approach to computations with singular potentials Original Research Article

We pioneered the application of the quasilinearization method (QLM) to the numerical solution of the Schrödinger equation with singular potentials. The spiked harmonic oscillator image is chosen as the simplest example of such potential. The QLM has been suggested recently for solving the Schrödinger equation after conversion into the nonlinear Riccati form. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. The choice of zero iteration is based on general features of solutions near the boundaries.