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NDEigensystem works fine for the following 3D Schrödinger equation

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 4D 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?

Domen
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L Pagnucco
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  • 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 01:07
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    I think FEM is the basis for NDEigensystem and it is restricted currently to dimensions 1, 2, and 3 -- see http://reference.wolfram.com/language/FEMDocumentation/tutorial/SolvingPDEwithFEM.html#1928222731 – Michael E2 May 20 '18 at 01:08
  • Might be possible to follow this post and do it by hand? https://mathematica.stackexchange.com/questions/84726/numerically-solving-helmholtz-equation-in-3d-for-arbitrary-shapes – chris Mar 20 '24 at 16:44

0 Answers0