Calculational approach for the structure of electron and hole levels in quantum dots of varying shape

Another approach to the calculation of electron and hole states in quantum dots is proposed. It benefits from the particular choice of products of powers of Cartesian coordinates as a basis, since it is possible to evaluate all required matrix elements analytically for these systems. A variety of dot shapes in the presence of external electric fields can be analyzed conveniently. This approach provides a way to calculate quantum dot ensemble averages quickly and effectively.