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

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.

References in corpus (1)

• Quasi-exact-solution of the Generalized Exe Jahn-Teller Hamiltonian

Cited by in corpus (4)

• Solution of a Hamiltonian of quantum dots with Rashba spin-orbit coupling: quasi-exact solution
• Algebraic treatments of the problems of the spin-1/2 particles in the one and two-dimensional geometry: a systematic study
• Solution of spin-boson systems in one and two-dimensional geometry via the asymptotic iteration method
• Solution of the Bosonic and Algebraic Hamiltonians by using AIM