Wolfram Language

Differential Eigensystems

Study a SturmLiouville System with Antiperiodic Boundary Conditions

Find the five smallest relational antiperiodic eigenvalues and eigenfunctions of a SturmLiouville operator.

Specify a SturmLiouville operator.

In[1]:=
Click for copyable input
V[x_] := Cos[x] + x; \[ScriptCapitalL] = -u''[x] - (V''[x] - V'[x]^2) u[x];

Specify a relational antiperiodic boundary condition.

In[2]:=
Click for copyable input
\[ScriptCapitalB] = PeriodicBoundaryCondition[-2 u[x], x == 2 \[Pi], TranslationTransform[{-2 \[Pi]}]];

Find the five smallest eigenvalues and eigenfunctions.

In[3]:=
Click for copyable input
{vals, funs} = NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x], {x, 0, 2 \[Pi]}, 5];

Inspect the eigenvalues.

In[4]:=
Click for copyable input
vals
Out[4]=

Visualize the eigenfunctions.

In[5]:=
Click for copyable input
Plot[funs, {x, 0, 2 \[Pi]}]
Out[5]=

Related Examples

de es fr ja ko pt-br ru zh