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

arXiv commentThis paper has been accepted by IJMPE ( as can be seen on their website) and given the doi number below

References in corpus (9)

• Low-energy enhancement of magnetic dipole radiation
• Large low-energy $M1$ strength for ${}^{56,57}$Fe within the nuclear shell model
• Low energy magnetic radiation enhancement in the f${}_{7/2}$ shell
• The Spin and Orbital Contributions to Magnetic Dipole Transitions
• Matrix Model of Strength Distribution: Extension and Phase Transition
• Relation between exponential behavior and energy denominators -- Weak Coupling Limit
• Cascade Calculations with Schematic Interactions
• Wave Functions of Pentadiagonal Matrices in the Weak Coupling Limit
• Distribution of Magnetic Dipole Strength -Binning

Cited by in corpus (1)

• Comparisons of Matrices with Different Elements but Identical Eigenvalues