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This program runs fine and I am able to get eigenvalues and eigenfunctions, however, I want to give a range of values for x and y. Can you suggest, how to edit my code for that?

 \[ScriptCapitalR] = ImplicitRegion[x^2 + y^2 <= 1, {x, y}];

V[x_, y_] = If[{x, y} \[Element] Region[\[ScriptCapitalR]], 0, \[Infinity]];

{vals, funs} = NDEigensystem[{-Laplacian[u[x, y], {x, y}] + V[x, y]*u[x, y],DirichletCondition[u[x, y] == 0, True]}, u, {x, y} \[Element] Region[\[ScriptCapitalR]], 10, Method -> {"SpatialDiscretization" -> {"FiniteElement",\{"MeshOptions" -> {MaxCellMeasure -> 0.01}}}}];
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  • $\begingroup$ On what should the range depend? $\endgroup$
    – user21
    Commented Jan 11, 2022 at 6:35
  • $\begingroup$ range should depend on x and y $\endgroup$
    – user444
    Commented Jan 11, 2022 at 7:03
  • $\begingroup$ Well, yes, but how? $\endgroup$
    – user21
    Commented Jan 11, 2022 at 8:25
  • $\begingroup$ I need to specify a range of the values for x and y where I am writing {x,y} are elements of Region[R], in the last line. $\endgroup$
    – user444
    Commented Jan 18, 2022 at 4:37
  • $\begingroup$ Still unclear what you want to do, show the code that does not work. Maybe it is possible to infer what you would like to do from that. $\endgroup$
    – user21
    Commented Jan 18, 2022 at 5:58

1 Answer 1

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\[ScriptCapitalR] = ImplicitRegion[x^2 + y^2 <= 1, {x, y}];

V[x_, y_] = 
  If[{x, y} \[Element] Region[\[ScriptCapitalR]], 0, \[Infinity]];

{vals, funs} = 
  NDEigensystem[{-Laplacian[u[x, y], {x, y}] + V[x, y]*u[x, y], 
    DirichletCondition[u[x, y] == 0, True]}, 
   u, {x, y} \[Element] Region[\[ScriptCapitalR]], 10];

Table[Plot3D[
  funs[[i]][x, y], {x, y} \[Element] \[ScriptCapitalR]], {i, 10}]

enter image description here

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