Abstract In this thesis, we set the stage by investigating the quantum dynamics of linearly interacting quantum harmonic oscillators. For this purpose, we start with two interacting quantum harmonic oscillators with a time-dependent coupling function between them. Then, we generalize the problem to three and n linearly-interacting oscillators. We will obtain exact and explicit relations for ladder operators, reduced density matrices, and the generated states in the framework of Bogoliubov transformations. In the following, we will investigate the quantum state propagation along a quantum chain of n quantum harmonic oscillators.
