Numerical solution of schrodinger’s equation by lobatto quadrature method of sixth order

Abstract

The one dimensional time independent Schrodinger’s equation is a second order boundary value problem without the first order term explicitly. In this current study, the solution of the time independent Schrodinger’s equation is obtained using the Wood’s - Saxon Potential. The computation is done numerically by using a sixth order method based on Lobatto quadrature. This generates the different values of energies for the first six bound states after the same number of iterations as that of Numerov’s method. The resultsobtainedbyLobattoquadratureformulaarecomparedagainstthosefor Numerov’s method for the various values of the step lengths. This is done in terms of computation of the errors with respect to the analytical solutions. The magnitude of the errors for both methods indicates that Lobatto quadrature method yield values which have smaller errors than Numerov’s method when compared with the exact solutions.