Optimum Jastrow function for few-electron ground states in a quantum dot: Reduction to a three-particle problem.

Abstract

A new approach to calculating the optimum Jastrow wave function is presented for a system of $N$ electrons in a two-dimensional quantum dot. By introducing special derivative operators which act on differences of electron coordinates ${\mathbf{r}}_{\mathrm{ij}}={\mathbf{r}}_{i}\ensuremath{-}{\mathbf{r}}_{j}$ as if they were independent coordinates ${\mathbf{r}}_{\mathrm{ij}}}i<j$, it is shown that the problem of finding the optimum $N$-particle Jastrow function reduces to a three-particle problem (for$N\ensuremath{\ge}3$). This three-particle problem is then solved using a variational method to find the optimum pair function $\ensuremath{\varphi}({\mathbf{r}}_{\mathrm{ij}})$. A perpendiculat magnetic field may also be included in the problem.