Solution of the Bosonic and Algebraic Hamiltonians by using AIM

TL;DR

This paper demonstrates how the asymptotic iteration method (AIM) can be effectively used to find eigenvalues of complex bosonic Hamiltonians, including quantum optical models and Lie algebraic structures.

Contribution

It introduces a novel application of AIM to solve eigenvalue problems for a broad class of bosonic and algebraic Hamiltonians, including multi-boson systems.

Findings

Eigenvalues of bosonic Hamiltonians are obtained using AIM.

The method is applicable to quantum optical models and Lie algebraic structures.

Eigenvalues of multi-boson Hamiltonians are derived through transformation.

Abstract

We apply the notion of asymptotic iteration method (AIM) to determine eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider solutions of the Hamiltonians, which are even polynomials of the fourth order with the respect to Boson operators. We also demonstrate applicability of the method for obtaining eigenvalues of the simple Lie algebraic structures. Eigenvalues of the multi-boson Hamiltonians have been obtained by transforming in the form of the single boson Hamiltonian in the framework of AIM.