The issue in your code is related to variable scoping. Inside the Do loop, you are using the variable testWaveFunctions which is also defined outside the loop. This can lead to conflicts and unintended behavior.

To fix this issue, you can use a different variable inside the loop. Here's an updated version of your code:

(* Test *)
testN = List[1, 2];
test[x_, y_, z_, t_] := testN[[y]]*testN[[z]]*(x + y + z + t)

Do[
  Module[{testMatrix, testMatrixSummed, testValues, localWaveFunctions, localTestN},
    testMatrix = Table[Table[test[x, y, z, t], {y, {1, 2}}, {z, {1, 2}}], {x, {1, 2}}, {t, {1, 2}}];
    testMatrixSummed = Table[Total[testMatrix[[i, j]], 2], {i, 1, 2}, {j, 1, 2}];
    testValues = Eigenvalues[testMatrixSummed];

    localWaveFunctions = Eigenvectors[testMatrixSummed];
    localTestN = N[localWaveFunctions[[Min[Position[testValues, Min[testValues]]]]]];

    (* Use localWaveFunctions and localTestN as needed *)
    Print[localWaveFunctions];
    Print[localTestN];
  ],
  2
]

In this modification, I introduced localWaveFunctions and localTestN inside the Module to ensure that they are local to each iteration of the loop. This avoids conflicts with the variables defined outside the loop. Adjust the usage of these local variables as needed within the loop.

When you put your code in two cells did you first click to put the cursor in the first cell and press <shift><enter> and then click to put the cursor in the second cell and then press <shift><enter>?

Doing those steps in that order will instruct Mathematica to evaluate your first cell and initialize any variables in it and then evaluate your second cell which uses the definitions and values of the first cell.

You can try an experiment. Start Mathematica fresh. In the first cell put x=2, but do not do <shift><enter>. In the second cell put Print[x] and follow that with <shift><enter>. I believe that should not print 2. Then repeat this experiment with a fresh start of Mathematica. x=2 <shift><enter> for the first cell and Print[x] <shift><enter> for the second cell and I believe that should print 2. There is a hidden cache in Mathematica that keeps the information from previously evaluated cells, unless you ask it to remove some or all information in the cache.

From your first question, I am guessing it would be fine to add another question onto the end of this. If the question is on a very different problem then perhaps a new question might be better.

Thank you Bill. It works.

If it is possible Can I ask one more question down here? Or should I close this one? And open another discussion?