# NDEigensystem works for 3-D Schrodinger Equation but not 4-D

NDEigensystem works fine for the following 3-D Schrodinger Equation code -- Clear["Global*"] Rcube = ImplicitRegion[-1 <= x <= 1 && -1 <= y <= 1 && -1 <= z <= 1, {x, y, z}]; NDEigensystem[{-Laplacian[u[x, y, z], {x, y, z}] + Boole[x + y + z > -2]*u[x, y, z], DirichletCondition[u[x, y, z] == 0, True]}, u, Element[{x, y, z}, Rcube], 3]

But when it is generalized to 4-D as follows --

Rcube = ImplicitRegion[-1 <= w <= 1 && -1 <= x <= 1 && -1 <= y <= 1 && -1 <= z <= 1, {w, x, y, z}]; NDEigensystem[{-Laplacian[u[w, x, y, z], {w, x, y, z}] + Boole[w + x + y + z > -2]*u[w, x, y, z], DirichletCondition[u[w, x, y, z] == 0, True]}, u, Element[{w, x, y, z}, Rcube], 3]

-- it fails. Why?

• You can format inline code and code blocks by selecting the code and clicking the {} button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful – Michael E2 May 20 '18 at 1:07
• I think FEM is the basis for NDEigensystem` and it is restricted currently to dimensions 1, 2, and 3 -- see reference.wolfram.com/language/FEMDocumentation/tutorial/… – Michael E2 May 20 '18 at 1:08