I am relatively new to Mathematica and have been trying to use the NDEigensystem command to work with some quantum systems. I am able to get the accurate energy eigenvalues but am having problems with eigenfunctions; more specifically, I am having trouble actually calling values using the interpolating functions.
m2 = 0.5;
ℏ = 1;
w = 0.5;
\[ScriptCapitalO]2 = -ℏ^2/(2 m2) Laplacian[u[x, y], {x, y}] +
1/2 m2 w^2 (x^2 + y^2) u[x, y];
{vals, funs} =
NDEigensystem[{\[ScriptCapitalO]2,
DirichletCondition[u[x, y] == 0, True]},
u[x, y], {x, -10, 10}, {y, -10, 10}, 28,
Method -> {"PDEDiscretization" -> {"FiniteElement", {"MeshOptions" \
-> {"MaxCellMeasure" -> 0.5}}}}];
As we can see above, I am using a simple 2d harmonic oscillator as my Hamiltonian, and then using the NDEigensystem command I am generating eigenvalues and eigenfunctions. I am able to get the right eigenvalues for my system as we can see below
However; the eigenfunctions aren't usable, I am trying to extract the data from the interpolating functions to no avail. From what I understand the syntax is:
ψ = funs[[1]]
ψ[2,3]
The above code should print the values of the first eigenfunction as {2,3} but it doesn't seem to be working. I'm hoping to eventually integrate these functions to calculate expectation values, I would be very grateful for any help or advice.