Nodal Surfaces of Degenerate States

Nodal surface of a degenerate state in an 3D infinite square potential well. Degenerate solutions of an eigenvalue problem are linearly independent solutions to the same eigenvalue. For the Helmholtz equation within a cubical box with homogeneous Dirichlet boundary conditions, most states have sixfold degeneracy. This Demonstration allows the exploration of the space of possible nodal surfaces for a low-lying state. The nodal surface is the eigenfunction zero locus.