Time advancement of relevant administrators in the Rabi Hamiltonian and its pivoting wave estimation (RWA) adaptation, the Jaynes-Cummings Model (JCM), in the Heisenberg picture, gives frameworks of Nonlinear Differential Conditions (NDEs). Thinking about all-around restricted particles, the Mean-Field Hypothesis (MFT) was applied to supplant the administrators by comparable assumption values. The Rabi model was decreased to a fourth orders NDE depicting particles position. Arrangement by the consonant equilibrium technique (HBM) showed great precision and consistency to the mathematical outcomes, which presents it as a valuable instrument in quantum elements studies. The NDEs portraying the JCM in the Heisenberg picture primarily forestall applying the MFT and shows irregularity to Ehrenfest's hypothesis, in spite of the Rabi model.
