求薛定谔算子的谱
在一个一维区域上求解薛定谔方程 的特征值问题.
设定一个无约束的薛定谔算子.
In[1]:=
![Click for copyable input](assets.zh/find-the-spectrum-of-a-schrdinger-operator/In_10.png)
h = 1/10; V[x_] := x^2
\[ScriptCapitalL] = -h^2*u''[x] + V[x]*u[x];
在细化网格上找出最小的 10 个特征值和特征函数.
In[2]:=
![Click for copyable input](assets.zh/find-the-spectrum-of-a-schrdinger-operator/In_11.png)
{vals, funs} =
NDEigensystem[\[ScriptCapitalL], u[x], {x, -3, 3}, 10,
Method -> {"SpatialDiscretization" -> {"FiniteElement", \
{"MeshOptions" -> {MaxCellMeasure -> 0.01}}}}];
查看特征值.
In[3]:=
![Click for copyable input](assets.zh/find-the-spectrum-of-a-schrdinger-operator/In_12.png)
vals
Out[3]=
![](assets.zh/find-the-spectrum-of-a-schrdinger-operator/O_6.png)
可视化特征函数. 特征函数按 标度,并按各自的特征值做了平移.
显示完整的 Wolfram 语言输入
Out[4]=
![](assets.zh/find-the-spectrum-of-a-schrdinger-operator/O_7.png)