Spectra of Equilateral Graphs

eigvals_quantum(Γ::EquilateralMetricGraph; K=3, sorted=true, only_vertex=false)

Compute all eigenvalues $\lambda < ('K' \pi)/ \ell)^2$ of the equilateral metric graph 'Γ'.

eigen_quantum(Γ::EquilateralMetricGraph; K=3, sorted=true, sparse_svd=false)

Compute all eigenvalues $\lambda < ('K' \pi)/ \ell)^2$ and corresponding eigenfunctions $\phi$ with

\[{\phi}_e = A_e \cos(\sqrt{\lambda} x) + B_e \sin (\sqrt{\lambda} x)\]

of the equilateral metric graph 'Γ'.

The coefficient $A_e$, $B_e$ are stored in A = [Ae1,…,Aem]' and B = [Be1,…,Bem]' for each eigenfunction. The coefficients are normalized such that all eigenfunctions fulfill $\| \phi \|=1$.

count_eigvals_K(Γ::EquilateralMetricGraph, K::Int)

Return number of eigenvalues $\lambda < ('K'* \pi/ \ell)^2$.