one hundred or more times larger than the atoms. Thus, in addition to atoms, nuclei,$\cdot \cdot \cdot $ that exist in nature, quantum dots as a new kind of system will definitely contain new and rich physics, and therefore they attract certainly the interest of academic research.

  On the other hand, the properties of the dots can be changed  in a controlled way, e.g., by changing the gate voltage or by applying an adjustable magnetic field, etc. Therefore, these systems  have a great potential in application. Due to this fact, the investigation of quantum dots is a hot topic in recent years$^{1-6}$.  In the experimental aspect, progress has been made to reveal different kinds of physical property. A crucial point is to clarify the electronic structures. An important step along this line is the first observation of the Coulomb blockade spectra via the measurement  of conductance as a function of gate voltage$^{7}$, where very clear level structure has been demonstrated. Afterwards, a substantial amount of information is drawn from conductance measurement.  The measurement of the difference in chemical potential exhibits also clear shell structures$^{8}$.  The excitation of electron can be probed by far-infrared and capacitance spectroscopy.$^{9,10}$  With further progress in 