Computing the -Numerical Range of Differential Operators

Figure 1

On the left-hand side, the variational method approximation to the Schrödinger operator. The approximation is given by a self-adjoint matrix with some real eigenvalues with The -numerical range of for is the line segment ; the red dots are . On the right-hand side, the -numerical range of for is the union of the closed circular discs. The small red circles on the real axis inside the circular disk are scaled by .