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) Twoenergy-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 T_0=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. 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) Twoenergy-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 (iii) Due to the confinement that is a two dimensional xy plane symmetric structure in the AGPQW and the asymmetrical Gaussian potential (AGP) T_0 = 22.475 fs. in the AGPQW growth direction, the electron probability density presents only one peak configuration located in the coordinate of z> 0, but it 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, it it an increasing one in the confinement potential R> 0.24 nm and it takes a minimum value in R = 0.24 nm.