Differential realizations of the two-mode bosonic and fermionic Hamiltonians: A unified approach

摘要

A method is developed to determine the eigenvalues and eigenfunction of two-boson 2 x 2 matrix Hamiltonians that include a wide class of quantum optical models. The quantum Hamiltonians are transformed in the form of the one variable differential equation and the conditions for their solvability are discussed. We present two different transformation procedures 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.