I am trying to diagonalize the Bogoliubov-de Gennes Hamiltonian. The problem is that the Hamiltonian contains a Laplacian. This could be solved by using a discretized Laplacian

If I use a simple Hamiltonian (just the Laplacian) and use eig(l1dd(...,...)) with l1dd the discretized Laplacian (2 and -1's) as in https://people.sc.fsu.edu/~jburkardt/m_src/laplacian/laplacian.html, Then I get:

I expect a linear or quadratic dispersion ($\omega \propto k or k^2$), but I get neither. What could be the problem? It seems that eig does a good job, so probably l1dd is the problem?