Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach

TL;DR

This paper introduces a unified method to solve two-mode bosonic and fermionic Hamiltonians, transforming them into differential equations, and applies it to models like Jaynes-Cummings and Jahn Teller.

Contribution

It develops a unified approach using differential equations and Lie algebraic techniques to analyze two-mode quantum Hamiltonians, encompassing various models.

Findings

Unified method for eigenvalues and eigenfunctions of two-mode Hamiltonians

Transformation procedures simplify complex quantum models

Application to Jaynes-Cummings and Jahn Teller models demonstrates effectiveness

Abstract

A method is developed to determine the eigenvalues and eigenfunction of two-boson $2\times 2$ matrix Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential equation and the conditions for its solvability have been discussed. We present two different transformation procedure and we show our approach unify various approaches based on Lie algebraic technique. As an application, solutions of the modified Jaynes-Cummings and two-level Jahn Teller Hamiltonians are studied.