MATSLISE: (Regular) Sturm-Liouville equation |
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The File-Menu
Closes the current Sturm-Liouville problem and opens a new problem: a Schrödinger problem, a new Sturm-Liouville problem or a a distorted Coulomb problem.
Open ProblemDisplays a dialog box that enables you to retrieve a problem which was saved earlier.
Some (test)problems are predefined in the directory
predefined_problems
.
Allows you to save the problem you defined. This saved
problem can then be re-opened later. All problems should be saved in an .mat
-file.
Please note that information about the problem can be entered in the text-field at the bottom of the Sturm-Liouville window. This information is also saved with the rest of the problem.
The Options-Menu
Show partitionWhen this option is checked, an additional plot is produced by the construct-button. On this plot the partition is displayed for the associated Schrödinger problem.
Half-range reductionHalf-range reduction can be applied to symmetric Sturm-Liouville problems.
A Sturm-Liouville problem is symmetric when the problem is posed on the interval -b
to b
, where b
may be inf
, and the coefficient functions
are even,
p(x)=p(-x), q(x)=q(-x), w(x)=w(-x),
and the boundary conditions are similarly symmetric, which means that
A0 = A1, B0 = -B1
.In this case the eigenfunctions belonging to eigenvalue E_k
(k=0,1,...
) are even or odd functions according as k
is even or odd. Hence, the eigenvalues can be obtained by solving the given equation, but
on the interval [0,b]
, with the given boundary condition at b
and with
y'(0) = 0
to get the even eigenvaluesy(0) = 0
to get the odd eigenvalues.The normalized eigenfunctions of the full-range problem are reconstructed from those of the
half-range problem by extending in the appropriate way and dividing by sqrt(2)
.
Reference: J. D. Pryce, Numerical Solution of Sturm-Liouville Problems (Oxford Univ. Press, Oxford, 1993), §2.5.2.
![]() | The construct-button | Distorted-Coulomb problem |
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