The relation of the energy of electronic state with the interior periodic potential in quantum dot given by matrix method

In this paper, we mainly investigate the effect of the interior periodic potential and the surface potential on the energy of electronic state in quantum dot. Based on Chebyshev polynomials of the second kind and matrix theory, we deduced one expression, which can clearly describe the relation of energy of electronic state with the surface and interior periodic potential. The theoretical analysis shows that the energy of electronic state in quantum dot strongly depend on surface potential and the interior periodic potential. For the same quantum dot with different surface potential, the energy of electronic state with the determined quantum number is different. For the quantum dot of same size with different interior periodic potential, the energy of electronic state with the determined quantum number is also different. The further study indicates that there are two different energy of electronic state in quantum dot for the decided quantum number.