The electronic structure and optical properties of a one-electron quantum dot (QD) were investigated by assuming a spherically symmetric confining potential of finite depth. In this particular case CdSe is surrounded by ZnS. The energy eigenvalues and wave functions dependence on QD dimension were calculated by using effective mass approximation. We also calculated energies of s, p, and d states, oscillator strengths, and the linear and third-order nonlinear intersubband optical absorption coefficients as a function of the QD dimension, incident photon energy, and incident optical intensity for the 1s-1p, 1p-1d, and 1p-2s transitions. Even in a simple composition, QD correct calculation of oscillator strength differs from the simplified approach in the most sensitive QD radius region below one Bohr radius.