MATSLISE: Calculating the eigenfunctions    

The Eigenfunctions window

This window is generated when the Eigenfunction-button in the Eigenvalues-window is clicked. All the selected eigenfunctions are plotted. For a Sturm-Liouville problem first the eigenfunctions of the associated Schrödinger problem are computed. These Schrödinger eigenfunctions are then transformed into the Sturm-Liouville eigenfunctions and displayed. This (Liouville) transformation is the reason why the computation of the eigenfunctions of a Sturm-Liouville problem needs in general more time than the computation of Schrödinger eigenfunctions.

The Select All-button

This selects all the entries in the eigenfunctions-list. An entry can also be selected using the SHIFT- and CTRL-keys.

The Test orthonormality-button

After the plotting it is possible to test the orthonormality of a selection of the eigenfunctions. The results of this test are then listed in the Results-box. e.g.:

Note1: For regular Sturm-Liouville problems <y_i,y_j> is the integral of y_i * y_j * w. (with w = w(x) see Sturm-Liouville problem )

Note2: The calculations are interrupted by a click on the stop-button.

Show with potential - button

With a click on the Show with potential-button the eigenfunctions-potential plot window is opened.

Show on same plot - button

With a click on this button, the selected eigenfunctions are displayed on one and the same plot.

Focus on one function - button

A new window is opened: Eigenfunction-plot window, where the selected eigenfunction is plotted.


Note: When one of the calculated eigenfunctions is not correct, i.e. when the eigenfunction corresponding to E_k has more or less than k zeros, an error message is displayed.


   The Eigenvalues window  Eigenfunction plot window