An isoperimetric problem for point interactions

Details An isoperimetric problem for point interactions An isoperimetric problem for point interactions

2004-06-10

arxiv.org/abs/math-ph/0406017v1

J. Phys. A38 (2005), 4795-4802

Physics

Mathematical Physics

LaTeX 2e, 10 pages

Scientific paper

10.1088/0305-4470/38/22/004

We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all
with the same coupling constant, placed at vertices of an equilateral polygon
$\PP_N$. It is shown that the ground state energy is locally maximized by a
regular polygon. The question whether the maximum is global is reduced to an
interesting geometric problem.

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