Matrix Model: Emergence of a Quantum Number in the Strong Coupling Regime

TL;DR

This paper investigates simple matrix models in quantum mechanics, revealing that in the strong coupling regime, wave functions can be classified into two types distinguished by a new quantum number, with implications for transition rates.

Contribution

It introduces a novel quantum number emerging in the strong coupling limit of matrix models, expanding understanding of their eigenfunctions and transition behaviors.

Findings

Wave functions split into two classes at strong coupling

A new quantum number distinguishes these classes

Implications for transition rate calculations

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 2 classes and we can assign a quantum number to distinguish them. Implications for transition rates are also discussed.