Variational reproducing kernel Hilbert space (RKHS) grid method for quantum mechanical bound-state problems

An efficient grid-based method is presented for numerically solving the bound-state Schrِdinger equation. The method is based on utilizing the reproducing kernel Hilbert space technique to accurately interpolate between grid points for wavefunctions. A reproducing kernel of simple form for solving bound-state problems is introduced in terms of an appropriate Greenʹs function, in conjunction with a simple and effective procedure for sampling unevenly spaced grid points. Numerical tests made on two model potentials demonstrate that the method can offer accurate results.