Variational Calculations of the Exchange Energy of a Two-Electron Quantum Dot in a Magnetic Field

The ground-state energies of a two-electron quantum dot are calculated using the variational calculation method to solve the relative part hamiltonian of a two-dimensional quantum dot presented in a uniform magnetic field. we have shown the dependence of the exchange energy of the two-electron quantum dot on the confining frequency and strength of the magnetic field. the transitions in the angular momentum and spin of the quantum dot ground state are also shown. based on comparisons with different works, the variational method gives very good results.