Low-energy states in a quantum dot obtained by the orbital integration method

[[abstract]]The ground-state energy of two electrons in a harmonic quantum dot is obtained by using the recently developed orbital integration method. Compared to other analytical methods previously used to study this system, this method is much simpler and the result is more accurate. However, in this method we can directly calculate the ground-state energy without solving for the corresponding wavefunction. The ground-state energy is represented as a systematic series in an analytic form and it converges very fast in the range of experimental interest. We find that without a magnetic field the ground state always has the azimuthal quantum number mφ = 0; this result is at variance with a previous work. The critical magnetic field for spin-singlet-triplet crossing for a quantum dot made of GaAs is also obtained. In addition, on the basis of this method a new trial wavefunction for the ground state is also examined.[[fileno]]2010128010015[[department]]物理