The Wigner-Fokker-Planck equation is a parabolic (in some cases degenerate parabolic) partial differential equation. It describes the time evolution in phase space of an ensemble of quantum particles under the influence of an exterior potential and interacting with a heat bath of harmonic oscillators in thermal equilibrium. In this work, we study the existence and the regularity of the solution of this equation for different exterior potentials: in Chapter 2 for a harmonic oscillator potential and in Chapter 3 for a harmonic oscillator potential with a bounded perturbation. In the first case, we show that the solution is smooth. In the second case, the solution is also smooth under assumptions on the regularity of the perturbation. To this end we use two approaches: on the one hand, the existence and the analyticity of the strongly continuous semigroup that solves the equation; on the other hand, the estimation of the norm of the derivatives of the solution.