By employing the Pekar variational method, the eigenenergies and eigenfunctions of the ground and first-excited states are obtained in a strong electron-longitudinal optical (LO) phonon coupling RbCl quantum pseudodot (QPD). A single qubit can be realized in this two-level quantum system. The electron probability density (EPD) oscillates in the RbCl QPD with a certain period. The investigated results show that the EPD rises with raising the chemical potential of the two-dimensional electron gas and the zero point of the pseudoharmonic potential, whereas it decays with increasing the polaron radius. However, the oscillating period (OP) possesses precisely the opposite characteristics. Through the results and analysis above, we find three ways to adjust the EPD and the OP via changing the chemical potential of the two-dimensional electron gas, the zero point of the pseudoharmonic potential, and the polaron radius.