Apologies for a boring question.
I am trying to modify the standard Mathematica example for my needs.
The only differences in my case are:
- A more complicated potential (double-well, grows rapidly).
-
I’m interested in small values of $ \hbar$ .
h = 0.01; V[x_] := -x^2 + x^6; \[ScriptCapitalL] = 3^(3/2)/2 (-h^2*u''[x] + V[x]*u[x]); xmax = 1.2; xmin = -xmax; {vals, funs} = NDEigensystem[\[ScriptCapitalL], u[x], {x, xmin, xmax}, 10, Method -> {"SpatialDiscretization" -> {"FiniteElement", {"MeshOptions" -> {MaxCellMeasure -> 0.05}}}}]; Show[Plot[Evaluate[h*funs + vals], {x, xmin, xmax}], Plot[V[x], {x, xmin, xmax}], PlotRange -> {{xmin, xmax}, {-.1, .2}}, AxesOrigin -> {-3, 0}]
As you will see, Mathematica is not finding the lowest energies. I’m wondering if anyone could suggest a possible solution. Not sure which options of NDEigensystem to adjust. (Or probably there’s a better way to solve the problem).
