Solving the time-dependent Schrodinger equation is essential for understanding the actual response of system to external stimuli. Especially, in the experimental point of view, everything we did during the experiment changes the Hamiltonian, so it is hard to explain the result without understanding the time-dependent Schrodinger equation. Unfortunately, however, there are few time-dependent Schrodinger equations which can be solved exactly and need some approximations to solve the problem. In this worksheet, we will explore another approximation called adiabatic approximation which can be used in large, but slow change of Hamiltonian by using the mathematical approach and demonstration with well-known systems. This worksheet uses the Maple Quantum Chemistry Toolbox.