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An isoperimetric problem for point interactions

Pavel Exner
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Abstract

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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Pavel Exner. 2004-06-10. An isoperimetric problem for point interactions. https://doi.org/10.1088/0305-4470%2F38%2F22%2F004

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