GREEN’S FUNCTIONS AND TRANSITION AMPLITUDES FOR TIME-DEPENDENT LINEAR HARMONIC OSCILLATOR WITH LINEAR TIME-DEPENDENT TERMS ADDED TO THE HAMILTONIAN

We calculate the Green’s function for the time-dependent linear harmonic oscillator with linear time-dependent terms added to the Hamiltonian and use it to calculate the transition amplitudes between states of the time-independent linear harmonic oscillator. In the absence of the linear terms, transitions are only allowed from even (odd) to even (odd) parity states. However, in the case when the linear terms are present, transitions from even (odd) to odd (even) states are also allowed.