Two Electron Quantum Dot - A Variational Treatment For The Ground State
  A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet transitions of the ground state take place, which are captured in our solution. Using the same variational technique we find corrections to wave function and energy and the transition field strengths in a realistic dot where electron wave function has a finite extent in the direction perpendicular to the x-y plane in which usually 2-D dot electrons are confined. Using the variational wave function we show that photoemission cross-section as a function of magnetic field has sharp discontinuities, which can be used for experimental verification of the singlet-triplet transitions. 
Subinoy Das, Pallab Goswami and J.K.Bhattacharjee