The present paper discusses quantitatively the energy-optical spectrum and the AB oscillation of a negatively charged exciton on a quantum ring, under the influence of an uniform external electric field. The calculated optical spectrum agrees well with the experimental measurement. A negatively charged exciton is a system of three charged objects, making the numerical computations difficult due to the large size of the basic vector set and the Hamiltonian matrix. In this paper, a method is proposed to select an appropriate basic vector set Γ(Ｋｍｉｎ, Ｋｍａｘ) in order to reduce the number of basic vectors and to ensure minimal error due to the selection of the basic vectors. To verify the reliability of the suggested basic vector set Γ(Ｋｍｉｎ, Ｋｍａｘ), the authors also proposed a method to analyze D(K) which is the weight of the K component of the basic vector. The kinetic energy term 〈T〉 and the Coulomb action term 〈V〉 in the Hamiltonian, as well as the relationship between the external electric field term 〈E〉 and the radius of the ring R, are also discussed.