Two-dimensional quantum-dot helium in a magnetic field: Variational theory

A trial wave function for two-dimensional quantum-dot helium in an arbitrary perpendicular magnetic field a system of two interacting electrons in a two-dimensional parabolic confinement potential is introduced. A key ingredient of this trial wave function is a Jastrow pair correlation factor that has a displaced Gaussian form. The above choice of the pair correlation factor is instrumental in assuring the overall quality of the wave function at all values of the magnetic field. Exact numerical diagonalization results are used to gauge the quality of the proposed trial wave function. We find out that this trial wave function is an excellent representation of the true ground state at all values of the magnetic field including weak or zero and strong magnetic fields.