# Analytic results for N particles with 1/r2 interaction in two dimensions and an external magnetic field.

@article{Johnson1995AnalyticRF, title={Analytic results for N particles with 1/r2 interaction in two dimensions and an external magnetic field.}, author={Johnson and Quiroga}, journal={Physical review letters}, year={1995}, volume={74 21}, pages={ 4277-4280 } }

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a $(2N-4)$-dimensional problem which is independent of $B$ and $\omega_0$. An exact, infinite set of relative mode excitations are obtained for any $N$. The $N=3$ problem reduces to that of a ficticious particle in a two-dimensional, non-linear potential of strength $\beta…

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