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I tried to solve Schrödinger equation in 3D box using the NDEigensystem. My code is: {vals, funs} = NDEigensystem[{-1/ 2 (Div[Grad[u[x, y, z], {x, y, z}], {x, y, z}]), DirichletCondition[u[x, y, z] == 0, True]}, u[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 2]; How I can extract the numerical values of the u[x,y,z]? For example u[0,0,0?]

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{vals, funs} = NDEigensystem[{-1/2 (Div[Grad[u[x, y, z], {x, y, z}], {x, y, z}]), 
  DirichletCondition[u[x, y, z] == 0, True]}, u[x, y, z], 
  {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 2];

Then the value of u[0,0,0] for the eigenstates are

Table[funs[[i, 0]][0, 0, 0], {i, Length[funs]}]
(* {0.353627, 0.000205384} *)

You can also plot the solution:

Table[DensityPlot3D[Abs@funs[[i]], {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
    PlotRange -> All, PlotLabel -> vals[[i]], 
    ImageSize -> Medium], {i, Length[vals]}] // Row

enter image description here

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  • $\begingroup$ Hi, thanks a lot for answer :) $\endgroup$ – hosein gholizade May 31 '16 at 7:38

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