Time-Dependent Perturbation Theory in Quantum Phase Space

Time-dependent perturbation theory is discussed within the quantum phase space representation as formulated by Torres-Vega and Frederick(T-F) and the quantum transition probability is studied. Time-dependent perturbation formula in T-F quantum phase space is established, in accordance with the calculation theory in T-F phase space. As an example, the one dimensional harmonic oscillator system, affected by an external electric field, is used to calculate in T-F phase space, the result indicate that the principle of the method is correct.Quantum transition probability of the systems first excited state in T-F phase space is discussed.