The probability density, the transition frequency and the longitudinal optical (LO) phonon spontaneous emission rate of electronic states in the two-parameter asymmetric Gaussian (AG) potential two-level system are studied by using the Pekar variational method, and their single-parameter parabolic potential approximation are discussed. Numerical results show that the selecting the two-parameter AG potential to describe the restricted effects of electron in quantum dot can more accurately reveal the quantization characteristics of the wave property of electronic states, the statistical regularity of electron motion and the LO phonons spontaneous emission rate, and the results given by the single parametric parabolic approximation are relatively sample and rough. The influence of dispersion and electron-phonon coupling of materials on the probability distribution, quantum transition frequency and the LO spontaneous emission rate in the two-level system cannot be ignored.