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By using a variational method of Pekar type, we investigate the effects of the hydrogen-like impurity and magnetic field on the electron's probability density (PD) and oscillating frequency (OF) of a RbCl quantum pseudodot qubit. Numerical results indicate that (1) the PD oscillates periodically; (2) the crest of the PD will decrease with increasing the cyclotron frequencies and the Coulombic impurity potential strength; (3) as the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential increases, PD's peaks will occur more frequently; (4) besides, Figs. 1b and 2b clearly show that in a single period the PD will decrease with increasing the cyclotron frequency and the Coulombic impurity potential strength when $$ t > 1.8\;\text{fs} $$ ; whereas the changing law is just the opposite when $$ t < 1.8\;\text{fs} $$ ; (5) the OF is an aggrandizing function of the strength of the Coulombic impurity potential, whereas it is a decaying one of the cyclotron frequencies of the magnetic field. The coherence of qubit is crucial to the investigations of quantum information and quantum computation, where the electron's PD, the OF and the coherence time are the physical quantities representing the properties of coherence. Our research results fine that by changing the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential one can adjust the electron's PD and the OF. [ABSTRACT FROM AUTHOR]