Energy spectra of the Schrödinger equation and the differential quadrature method

Computation of the Schrödinger Equation via the Discrete Derivatives Representation Method: Improvement of Solutions Using Particle Swarm Optimization

“…It is interesting to take the same case as in [1] of the quasi-exact solutions for the singular even-power anharmonic potential to cast a light on the previous and present results. ( ) ; , 0…”

“…With this potential, the results for the first three energy levels obtained by the present method, the [1], the numerical integration of the Schrödinger equation, and the introduction of an ansatz for the state-function [9] are listed in Table 2, where the error tolerance: TOL…”

“…Several different methods, analytical and numerical have also been formulated and modeled during the past decades for the study of the solutions of the wave equation with different structures. It is known also that for very limited potentials, Schrödinger equation is exactly solvable [1][2][3][4][5][6].…”

“…The latest numerical approach to date is the differential quadrature method [1] introduced for energy spectra estimate. It was first applied to Schrödinger equation in the linear case, where the solution is not correctly reproduced in the domain in which strong oscillations can arise, or simply for instance in the case of highly excited states.…”

A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: The Schrödinger equation

“…Over the past years, a great deal of approximate schemas and numerical approaches have appeared to calculate the quantum quantities of the Schrödinger equation for numerous potential functions [1][2][3][4][5][6][7][8][9][10][11][12][13]. The scope of this area remains until now a more active field of diverse problems.…”