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The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) withinteraction $\beta/r^2$ 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 $\omega_0$. Anexact, 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 $\beta$, subject to a ficticious magneticfield $B_{\rm fic}\propto J$, the relative angular momentum.Comment: To appear in Physical Review Letters (in press). RevTeX file. Two  figures available from n.johnson@physics.oxford.ac.uk or  lquiroga@cdcnet.uniandes.edu.c

physical review letters

Analytic Results for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">N</mml:mi></mml:math>Particles with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi>/</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">r</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Interaction in Two Dimensions and an External Magnetic Field

Analytic Results forNParticles with1/r2Interaction in Two Dimensions and an External Magnetic Field