Matrix model: Emergence of a quantum number in the strong coupling regime

Abstract

We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously, we considered the weak coupling limits of our models, we here address the more difficult strong coupling limits. We find that the wave functions fall into two classes and we can assign a quantum number to distinguish them. Implications for transition rates are also discussed.