Considering hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot(QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well(PCPW) and an asymmetric Gaussian functional confinement potential well(AGFCPW) serving as the transverse and longitudinal confinement potential, respectively. Based on the above two states, a two-level system is constructed. Then, the ...