in Quantum Mechanics called the Adiabatic Theorem. The Adiabatic Theorem states that a system will stay in its evolving eigenstate provided the Hamiltonian is changed sufficiently slowly. Test this claim using the parameters of [1c]: x = 0.1 w₁ and a = 0.001 w₁₁. You already have the numerical and perturbative solutions to this transition. Now generate a third plot by directly calculating the occupation of the lowest eigenstate of H = Ho + V in the basis of Ho. This should allow you to calculate the occupation probability of the excited state of Ho as a function of time. Plot this probability along with your numerical and perturbative results, and comment on what you find. Aside: This is not the same notion of "adiabatic" as in thermal systems. Vaik Ⓡ
Fig: 1