Two-electron quantum dot with soft-edge barrier

A variational formalism to calculate energies of 1s, 21p, and 23p levels of a spherical quantum dot containing two electrons is developed. We express correspondent wave functions as a product of combinations of exact one-particle orbitals and variationally determined envelope function that depends only on separation between particles. An Euler-Lagrange differential equation for this last function is solved by using the trigonometric sweep method. We present novel curves for 1s, 21p, and 23p energy states dependencies on the radius of the quantum dots with hard wall and soft-edge barrier potential shapes. The effect of the repulsive core on the energies of the low-lying states and the pair correlation function is also analyzed. It is shown that the probability distribution of the electron-electron separation in a quantum dot with repulsive core is modified essentially with the increase of the quantum dot dimension, making more probable the finding of two electrons on diametrically opposite sides of the repulsive core.