Eigen-equation of Electronic Energy in Quantum Dot

In this paper, we present one simple model of quantum dot to describe the potential. Based on the boundary continuity of wave function and its derivative, using the Chebyshev polynomial of the second kind and matrix theory, we deduced one eigen-equation of electronic energy which can clearly describe the relationship between the energy level and the surface potential in quantum dot. The further study shows that the eigen-equation of electronic energy is different when the material of quantum dot is different.