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We analyze transition probabilities of harmonic oscillator system with spatial LQC (Linear-Quadratic-Cubic) perturbation in time-dependent. This system initially was in the ground state with no perturbation at  t  &lt; 0, then at t ≥ 0, the system is perturbed by spacial LQC perturbation in time-dependent until t → ∞. We use the time-dependent perturbation theory to analyze this problem. In the initial state, before there is no perturbation, we define the ground state with the base ket of harmonic oscillator without perturbation. Next, when the perturbation is applied to the system, we compute the transition amplitude base on the system state presented above and then we get total wave function that depends on time. By getting this wave function, we can compute transition probability for the system. As a result, there are three transition probabilities, namely the transitions from the ground state to the first, second, and third excited state. There is no transition to others.

Transition probabilities of harmonic oscillator system with spatial Linear-Quadratic-Cubic (LQC) perturbation in time-dependent