Two and k-Photon Jaynes–Cummings Models and Dirac Oscillator Problem in Bargmann–Segal Representation

In this work, we show that the Bargmann–Segal representation is a very simple approach to obtain the energy eigenvalues of some two-level quantum systems. It is shown that for 2-photon and k-photon Jaynes–Cummings models, the Bargmann–Segal realization gives the same energy eigenvalue which obtained by Lie algebraic and the matrix methods. We also study the Dirac oscillator problem in this representation.