With the circumstance of the electron strongly coupled to LO-phonon and using the variational method of Pekar type (VMPT),we study the eigenenergies and the eigenfunctions (EE) of the ground and the first excited states (GFES) in a RbCl crystal asymmetric Gaussian potential quantum well (AGPQW).It concludes:(i) Two-energy-level of the AGPQW may be seen as a qubit.(ii) When the electron located in the superposition state of the two-energy-level system,the time evolution and the coordinate changes of the electron probability density oscillated periodically in the AGPQW with every certain period T0 =22.475 fs.(iii) Due to the confinement that is a two dimensional x-y plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential (AGP) in the AGPQW growth direction,the electron probability density presents only one peak configuration located in the coordinate of z ＞ 0,whereas it is zero in the range of z ＜ 0.(iv) The oscillatory period is a decreasing function of the AGPQW height and the polaron radius.(v) The oscillating period is a decreasing one in the confinement potential R ＜ 0.24 nm,whereas it is an increasing one in the confinement potential R ＞ 0.24 nm and it takes a minimum value in R =0.24 nm.