Question 05/02

LINE OF CHARGES

Consider N identical "charges" placed along a straight line. A pair of charges at positions x_i and x_j repel each other via potential -ln|x_i-x_j|. Each charge is attracted to the origin of coordinates by a parabolic potential x_i²/2. Show that the equilibrium positions of the charges are given by the zeroes of the Hermite polynomial H_N.

This problem was brought to our attention by M. Fogler.

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