Energy spectra of the Schrödinger equation and the differential quadrature method: Improvement of the solution using particle swarm optimization

In our earlier work, we have developed the differential quadratic method (DQ) to find the physical structures of the Schrödinger equation in which the interpolating points of Tchebychev have been used. In this paper the particle swarm optimization (PSO for short) has been suggested as a means to improve qualitatively the solutions. This approach is carefully handled and tested with some numerical examples.