球体に含まれるラプラス演算子の固有関数のギャラリーを作成する
3Dラプラス演算子を定義する.
In[1]:=
![Click for copyable input](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/In_127.png)
\[ScriptCapitalL] = -Laplacian[u[x, y, z], {x, y, z}];
同次ディリクレ境界条件を指定する.
In[2]:=
![Click for copyable input](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/In_128.png)
\[ScriptCapitalB] = DirichletCondition[u[x, y, z] == 0, True];
球体の中の固有値と固有関数を小さい方から16個求める.
In[3]:=
![Click for copyable input](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/In_129.png)
\[CapitalOmega] = Ball[{0, 0, 0}, 2];
In[4]:=
![Click for copyable input](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/In_130.png)
{vals, funs} =
DEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x, y, z], {x, y, z} \[Element] \[CapitalOmega], 16];
固有値はBesselJZeroで与えられる.
In[5]:=
![Click for copyable input](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/In_131.png)
vals[[1]] // TraditionalForm
Out[5]//TraditionalForm=
![](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/O_63.png)
固有関数のギャラリーを生成する.
完全なWolfram言語入力を表示する
Out[6]=
![](assets.ja/create-a-gallery-of-eigenfunctions-for-the-laplaci/O_64.png)