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.
Publisher
University of Nairobi