الفهرس 
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Abstract
In this thesis, we discussed many algebric solutions of the Jaynes-Cummings model (JCM), a key piece of research in the field of light-matter interactions.
JCM was extended in two separate ways in rotating wave approximation. The conservative JCM is one, and the time-position dependent JCM is another. For the conservative models, we demonstrated four alternative approaches, while the time-position dependent model was solved using three approaches.
Our first method, Fuji approach, uses the semiclassical Hamiltonian. When Stark shift and Kerr-like medium were present separately, we used the London and Stecholm approaches to solve the corresponding quantaized Hamiltonian respectively. We presented three distinct strategies to solve three different two level moving atom JCMs. In the first method, both the momentum and position operators are contained in the Hamiltonian, whereas in the second, only the position operator is presented. The final model is the JCM’s time-dependent coupling parameter. The entire eigenstate is yielded for two different cases.
Supersymmetric theory, a novel technique, is utilized to diagonalize the quantaized Hamiltonian and determine the system’s eigenstate and eigenvalue in the presence of Stark shift and a Kerr-like medium.
The master equation is derived under the Born and Markov approximation.