Solution of the Matrix Hamiltonians via asymptotic iteration method

TL;DR

This paper introduces an extension of the asymptotic iteration method to solve 2x2 matrix Hamiltonians in quantum optics, successfully computing eigenvalues for Rabi and Rashba Hamiltonians and offering a unified approach to existing and new results.

Contribution

The paper extends the asymptotic iteration method to matrix Hamiltonians, providing a new analytical tool for solving quantum optical models.

Findings

Eigenvalues of Rabi and Rashba Hamiltonians are computed.

The method reproduces previous results and yields new insights.

Potential for generalizing the approach to other Hamiltonians.

Abstract

A method is suggested to obtain solutions of the various quantum optical Hamiltonians in the framework of the asymptotic iteration method. We extend the notion of asymptotic iteration method to solve the 2 \times 2 matrix Hamiltonians. On a particular case, eigenvalues of the Rabi and Rashba Hamiltonians are computed. The method presented here reproduces a number of earlier results in a natural way as well as leads to a novel findings. Possible generalizations of the method are also suggested.