# How to give range of values while using NDEigensystem for a 2D Schrödinger equation?

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}}}}];

• On what should the range depend? Commented Jan 11, 2022 at 6:35
• range should depend on x and y Commented Jan 11, 2022 at 7:03
• Well, yes, but how? Commented Jan 11, 2022 at 8:25
• 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. Commented Jan 18, 2022 at 4:37
• 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. Commented Jan 18, 2022 at 5:58

\[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}]