Algebraic solution of the hamiltonians of the two level quantum optical systems

In this thesis an algebraic method is developed for solution of two-levelquantum optical problems based on su(2) and su(1; 1) Lie algebras. The methodprovides a general framework within which many related problems can similarlybe solved. We concentrate our attention to the solution of the Jaynes-CummingsHamiltonian, as well as other quantum optical Hamiltonians. It is shown thatthe solution of quantum optical problems can be reduced to a homogenousordinary di¤erential equation. Our systematic approach reproduces a numberof earlier results and also leads to some novelties. Most of the quantum opticalHamiltonians possess hidden group structure based on su(2) or su(1; 1) algebraand they can be treated in the framework of the quasi-exactly solvable problems.Furthermore construction of the quantum optical Hamiltonians using …nite-group invariance is discussed. Generalization of the method to the variousquantum physics problems is indicated.Key words: Exactly solvable systems, Lie algebraic methods, Quantumoptical systems1