Sudden and Adiabatic Changes with Time

Fast and slow changes in Hamiltonian with time are treated as sudden and adiabatic approximations respectively. State of a system does not change instantaneously following an ideal sudden change. For an infinitely slow change, the system continuously adjusts to the instantaneous Hamiltonian, remaining in the same state of excitation. Sudden or adiabatic change is decided by comparing the duration of appreciable change with characteristic time of the system. Adiabatic theorem has been stated. Probability of transition to other than initial state calculated for adiabatic approximation. Examples are presented for sudden and gradual shifts of equilibrium point of a simple harmonic oscillator.